Q1. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = x2 - 2x - 5
a. maximum; 1
b. minimum; 1
c. maximum; - 6
d. minimum; - 6
Q2. Find the domain of the rational function.
g(x) =
a. all real numbers
b. {x|x ≠ -7, x ≠ 7, x ≠ -5}
c. {x|x ≠ -7, x ≠ 7}
d. {x|x ≠ 0, x ≠ -49}
Q3. Solve the inequality.
(x - 5)(x2 + x + 1) > 0
a. (-∞, -1) or (1, ∞)
b. (-1, 1)
c. (-∞, 5)
d. (5, ∞)
Q4. Find the domain of the rational function.
f(x) =
a. {x|x ≠ -3, x ≠ 5}
b. {x|x ≠ 3, x ≠ -5}
c. all real numbers
d. {x|x ≠ 3, x ≠ -3, x ≠ -5}
Q5. Solve the equation in the real number system.
x3 + 9x2 + 26x + 24 = 0
a. {-4, -2, -3}
b. {2, 4}
c. {3, 2, 4}
d. {-4, -2}
Q6. Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1.
a. -3
b. -2
c. 3
d. 2
Q7. Use the Theorem for bounds on zeros to find a bound on the real zeros of the polynomial function.
f(x) = x4 + 2x2 - 3
a. -4 and 4
b. -3 and 3
c. -6 and 6
d. -5 and 5
Q8. Find all zeros of the function and write the polynomial as a product of linear factors.
f(x) = 3x4 + 4x3 + 13x2 + 16x + 4
a. f(x) = (3x - 1)(x - 1)(x + 2)(x - 2)
b. f(x) = (3x + 1)(x + 1)(x + 2i)(x - 2i)
c. f(x) = (3x - 1)(x - 1)(x + 2i)(x - 2i)
d. f(x) = (3x + 1)(x + 1)(x + 2)(x - 2)
Q9. Find the power function that the graph of f resembles for large values of |x|.
f(x) = -x2(x + 4)3(x2 - 1)
a. y = x7
b. y = -x7
c. y = x3
d. y = x2
Q10. Use the Factor Theorem to determine whether x - c is a factor of f(x).
8x3 + 36x2 - 19x - 5; x + 5
a. Yes
b. No
Q11. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
f(x) = 9x3 + 8x2 - 6
a. No; the last term has no variable
b. Yes; degree 5
c. Yes; degree 3
d. Yes; degree 6
Q12. Solve the equation in the real number system.
x4 - 3x3 + 5x2 - x - 10 = 0
a. {-1, -2}
b. {1, 2}
c. {-1, 2}
d. {-2, 1}
Q13. A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 320 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?
a. 25,600 ft2
b. 19,200 ft2
c. 12,800 ft2
d. 6400 ft2
Q14. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
f(x) =
a. Yes; degree 3
b. No; x is a negative term
c. No; it is a ratio
d. Yes; degree 1
Q15. Give the equation of the oblique asymptote, if any, of the function.
h(x) =
a. y = 4x
b. y = 4
c. y = x + 4
d. no oblique asymptote
Q16. Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers.
f(x) = 3x4 - 6x3 + 4x2 - 2x + 1
a. no real roots; f(x) = (x2 + 1)(3x2 + 1)
b. 1, multiplicity 2; f(x) = (x - 1)2(3x2 + 1)
c. -1, 1; f( ...
Please be sure to save at least once every 15 minutes. If you leav.docxrandymartin91030
Please be sure to save at least once every 15 minutes. If you leave this page without saving, or if your session times out, any answers you have not saved will be lost. The Submit for Grading button will become available once you've answered all questions. Exams are not timed; you do not have to finish an exam in one sitting as long as you have saved your answers.
Q1. Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1.
a. -3
b. -2
c. 3
d. 2
Q2. Solve the inequality.
(x - 5)(x2 + x + 1) > 0
a. (-∞, -1) or (1, ∞)
b. (-1, 1)
c. (-∞, 5)
d. (5, ∞)
Q3. Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.
f(x) = 8x3 - 10x2 + 3x + 5; [-1, 0]
a. f(-1) = -16 and f(0) = -5; no
b. f(-1) = -16 and f(0) = 5; yes
c. f(-1) = 16 and f(0) = -5; yes
d. f(-1) = 16 and f(0) = 5; no
Q4. Solve the equation in the real number system.
x4 - 3x3 + 5x2 - x - 10 = 0
a. {-1, -2}
b. {1, 2}
c. {-1, 2}
d. {-2, 1}
Q5. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = x2 - 2x - 5
a. maximum; 1
b. minimum; 1
c. maximum; - 6
d. minimum; - 6
Q6. Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither.
f(x) = a. symmetry with respect to the origin
b. symmetry with respect to the y-axis
c. neither
Q7. Find the domain of the rational function.
f(x) = .
a. {x|x ≠ -3, x ≠ 5}
b. {x|x ≠ 3, x ≠ -5}
c. all real numbers
d. {x|x ≠ 3, x ≠ -3, x ≠ -5}
Q8. Find the domain of the rational function.
g(x) = a. all real numbers
b. {x|x ≠ -7, x ≠ 7, x ≠ -5}
c. {x|x ≠ -7, x ≠ 7}
d. {x|x ≠ 0, x ≠ -49}
Q9. Find all zeros of the function and write the polynomial as a product of linear factors.
f(x) = 3x4 + 4x3 + 13x2 + 16x + 4
a. f(x) = (3x - 1)(x - 1)(x + 2)(x - 2)
b. f(x) = (3x + 1)(x + 1)(x + 2i)(x - 2i)
c. f(x) = (3x - 1)(x - 1)(x + 2i)(x - 2i)
d. f(x) = (3x + 1)(x + 1)(x + 2)(x - 2)
Q10. Use the graph to find the vertical asymptotes, if any, of the function.
a. y = 0
b. x = 0, y = 0
c. x = 0
d. none
Q11. Find the power function that the graph of f resembles for large values of |x|.
f(x) = (x + 5)2
a. y = x10
b. y = x25
c. y = x2
d. y = x5
Q12. Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither.
f(x) = a. symmetry with respect to the y-axis
b. symmetry with respect to the origin
c. neither
Q13. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = -x2 - 2x + 2
a. minimum; - 1
b. maximum; 3
c. minimum; 3
d. maximum; - 1
Q14. Find the power function that the graph of f resembles for large values of |x|.
f(x) = -x2(x + 4)3(x2 - 1)
a. y = x7.
MATH 107 FINAL EXAMINATIONMULTIPLE CHOICE1. Deter.docxTatianaMajor22
MATH 107 FINAL EXAMINATION
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function.
A. Domain [–2, 2];
B. Domain [–1, 1];
C. Domain [–1, 3];
D. Domain [–3/2, –1/2];
2. Solve:
A. 3
B. 3,7
C. 9
D. No solution
3. Determine the interval(s) on which the function is increasing.
A. (−1.3, 1.3)
B. (1, 3)
C. (−∞,−1)and (3,∞)
D. (−2.5, 1)and (4.5,∞)
4. Determine whether the graph of y = 2|x| + 1 is symmetric with respect to the origin,
the x-axis, or the y-axis.
A. symmetric with respect to the origin only
B. symmetric with respect to the x-axis only
C. symmetric with respect to the y-axis only
D. not symmetric with respect to the origin, not symmetric with respect to the x-axis, and
not symmetric with respect to the y-axis
5. Solve, and express the answer in interval notation: | 9 – 7x | ≤ 12.
A. (–∞, –3/7]
B. (–∞, −3/7] ∪ [3, ∞) C. [–3, 3/7]
D. [–3/7, 3]
6. Which of the following represents the graph of 7x + 2y = 14 ?
A. B.
C. D.
7. Write a slope-intercept equation for a line parallel to the line x – 2y = 6 which passes through the point (10, – 4).
A.
B.
C.
D.
8. Which of the following best describes the graph?
A. It is the graph of a function and it is one-to-one.
B. It is the graph of a function and it is not one-to-one.
C. It is not the graph of a function and it is one-to-one.
D. It is not the graph of a function and it is not one-to-one.
9. Express as a single logarithm: log x + log 1 – 6 log (y + 4)
A.
B.
C.
D.
10. Which of the functions corresponds to the graph?
A.
B.
C.
D.
11. Suppose that a function f has exactly one x-intercept.
Which of the following statements MUST be true?
A. f is a linear function.
B. f (x) ≥ 0 for all x in the domain of f.
C. The equation f(x) = 0 has exactly one real-number solution.
D. f is an invertible function.
12. The graph of y = f(x) is shown at the left and the graph of y = g(x) is shown at the right. (No formulas are given.) What is the relationship between g(x) and f(x)?
y = f (x) y = g(x)
A. g(x) = f (x – 3) + 1
B. g(x) = f (x – 1) + 3
C. g(x) = f (x + 3) – 1
D. g(x) = f (x + 1) .
1. Write an equation in standard form of the parabola that has th.docxKiyokoSlagleis
1.
Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x
2
, but with the given point as the vertex (5, 3).
A. f(x) = (2x - 4) + 4
B. f(x) = 2(2x + 8) + 3
C. f(x) = 2(x - 5)
2
+ 3
D. f(x) = 2(x + 3)
2
+ 3
2 of 20
5.0 Points
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
f(x) = 2(x - 3)
2
+ 1
A. (3, 1)
B. (7, 2)
C. (6, 5)
D. (2, 1)
3 of 20
5.0 Points
Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.
g(x) = x + 3/x(x + 4)
A. Vertical asymptotes: x = 4, x = 0; holes at 3x
B. Vertical asymptotes: x = -8, x = 0; holes at x + 4
C. Vertical asymptotes: x = -4, x = 0; no holes
D. Vertical asymptotes: x = 5, x = 0; holes at x - 3
4 of 20
5.0 Points
"Y varies directly as the n
th
power of x" can be modeled by the equation:
A. y = kx
n
.
B. y = kx/n.
C. y = kx
*n
.
D. y = kn
x
.
5 of 20
5.0 Points
40 times a number added to the negative square of that number can be expressed as:
A.
A(x) = x
2
+ 20x.
B. A(x) = -x + 30x.
C.
A(x) = -x
2
- 60x.
D.
A(x) = -x
2
+ 40x.
6 of 20
5.0 Points
The graph of f(x) = -x
3
__________ to the left and __________ to the right.
A. rises; falls
B. falls; falls
C. falls; rises
D. falls; falls
Solve the following formula for the specified variable:
V = 1/3 lwh for h
7 of 20
Write an equation that expresses each relationship. Then solve the equation for y.
x varies jointly as y and z
A. x = kz; y = x/k
B. x = kyz; y = x/kz
C. x = kzy; y = x/z
D. x = ky/z; y = x/zk
8 of 20
8 times a number subtracted from the squared of that number can be expressed as:
A. P(x) = x + 7x.
B.P(x) = x
2
- 8x.
C. P(x) = x - x.
P(x) = x
2
+ 10x.
9of 20
Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.
f(x) = x
4
- 9x
2
A. x = 0, x = 3, x = -3; f(x) crosses the x-axis at -3 and 3; f(x) touches the x-axis at 0.
B. x = 1, x = 2, x = 3; f(x) crosses the x-axis at 2 and 3; f(x) crosses the x-axis at 0.
C. x = 0, x = -3, x = 5; f(x) touches the x-axis at -3 and 5; f(x) touches the x-axis at 0.
D. x = 1, x = 2, x = -4; f(x) crosses the x-axis at 2 and -4; f(x) touches the x-axis at 0.
10 of 20
Find the domain of the following rational function.
f(x) = x + 7/x
2
+ 49
A. All real numbers < 69
B. All real numbers > 210
C. All real numbers ≤ 77
D. All real numbers
11 of 20
Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x
2
or g(x) = -3x
2
, but with the given maximum or minimum.
Minimum = 0 at x = 11
A. f(x) = 6(x - 9)
B. f(x) = 3(x - 11)
2
C. f(x) = 4(x + 10)
D. f(x) = 3(x
2
- 15)
2
12 of 20
Solve the following polynomial inequality.
3x
2
+ 10x - 8 ≤ 0
A. [6, 1/3]
B. [-4, 2/3]
C. [-9, 4/5]
D. [8, 2/7]
13 of 20
Find the coordinate.
1) Use properties of logarithms to expand the following logarit.docxhirstcruz
1) Use properties of logarithms to expand the following logarithmic expression as much as possible.
Log
b
(√xy
3
/ z
3
)
A. 1/2 log
b
x - 6 log
b
y + 3 log
b
z
B. 1/2 log
b
x - 9 log
b
y - 3 log
b
z
C. 1/2 log
b
x + 3 log
b
y + 6 log
b
z
D. 1/2 log
b
x + 3 log
b
y - 3 log
b
z
2) Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution.
2 log x = log 25
A. {12}
B. {5}
C. {-3}
D. {25}
3) Write the following equation in its equivalent logarithmic form.
2
-4
= 1/16
A. Log
4
1/16 = 64
B. Log
2
1/24 = -4
C. Log
2
1/16 = -4
D. Log
4
1/16 = 54
4) Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.
log
2
96 – log
2
3
A. 5
B. 7
C. 12
D. 4
5) Use the exponential growth model, A = A
0
e
kt
, to show that the time it takes a population to double (to grow from A
0
to 2A
0
) is given by t = ln 2/k.
A. A
0
= A
0
e
kt
; ln = e
kt
; ln 2 = ln e
kt
; ln 2 = kt; ln 2/k = t
B. 2A
0
= A
0
e; 2= e
kt
; ln = ln e
kt
; ln 2 = kt; ln 2/k = t
C. 2A
0
= A
0
e
kt
; 2= e
kt
; ln 2 = ln e
kt
; ln 2 = kt; ln 2/k = t
D. 2A
0
= A
0
e
kt
; 2 = e
kt
; ln 1 = ln e
kt
; ln 2 = kt; ln 2/k = t
oe
6) Find the domain of following logarithmic function.
f(x) = log (2 - x)
A. (∞, 4)
B. (∞, -12)
C. (-∞, 2)
D. (-∞, -3)
7) An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e -0.000121t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in 5715 years?
A. Approximately 7 grams
B. Approximately 8 grams
C. Approximately 23 grams
D. Approximately 4 grams
8) Use properties of logarithms to expand the following logarithmic expression as much as possible.
log
b
(x
2
y) / z
2
A. 2 log
b
x + log
b
y - 2 log
b
z
B. 4 log
b
x - log
b
y - 2 log
b
z
C. 2 log
b
x + 2 log
b
y + 2 log
b
z
D. log
b
x - log
b
y + 2 log
b
z
9) The exponential function f with base b is defined by f(x) = __________, b > 0 and b ≠ 1. Using interval notation, the domain of this function is __________ and the range is __________.
A. bx; (∞, -∞); (1, ∞)
B. bx; (-∞, -∞); (2, ∞)
C. bx; (-∞, ∞); (0, ∞)
D. bx; (-∞, -∞); (-1, ∞)
10) Approximate the following using a calculator; round your answer to three decimal places.
3
√5
A. .765
B. 14297
C. 11.494
D. 11.665
11) Write the following equation in its equivalent exponential form.
4 = log
2
16
A. 2 log
4
= 16
B. 2
2
= 4
C. 4
4
= 256
D. 2
4
= 16
12) Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
3
1-x
= 1/27
A. {2}
B. {-7}
C. {4}
D. {3}
13) Use properties of logarithms to expand the followin.
1) Use properties of logarithms to expand the following logarithm.docxdorishigh
1) Use properties of logarithms to expand the following logarithmic expression as much as possible.
Logb (√xy3 / z3)
A. 1/2 logb x - 6 logb y + 3 logb z
B. 1/2 logb x - 9 logb y - 3 logb z
C. 1/2 logb x + 3 logb y + 6 logb z
D. 1/2 logb x + 3 logb y - 3 logb z
2) Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution.
2 log x = log 25
A. {12}
B. {5}
C. {-3}
D. {25}
3) Write the following equation in its equivalent logarithmic form.
2-4 = 1/16
A. Log4 1/16 = 64
B. Log2 1/24 = -4
C. Log2 1/16 = -4
D. Log4 1/16 = 54
4) Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.
log2 96 – log2 3
A. 5
B. 7
C. 12
D. 4
5) Use the exponential growth model, A = A0ekt, to show that the time it takes a population to double (to grow from A0 to 2A0 ) is given by t = ln 2/k.
A. A0 = A0ekt; ln = ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t
B. 2A0 = A0e; 2= ekt; ln = ln ekt; ln 2 = kt; ln 2/k = t
C. 2A0 = A0ekt; 2= ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t
D. 2A0 = A0ekt; 2 = ekt; ln 1 = ln ekt; ln 2 = kt; ln 2/k = toe
6) Find the domain of following logarithmic function.
f(x) = log (2 - x)
A. (∞, 4)
B. (∞, -12)
C. (-∞, 2)
D. (-∞, -3)
7) An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e -0.000121t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in 5715 years?
A. Approximately 7 grams
B. Approximately 8 grams
C. Approximately 23 grams
D. Approximately 4 grams
8) Use properties of logarithms to expand the following logarithmic expression as much as possible.
logb (x2 y) / z2
A. 2 logb x + logb y - 2 logb z
B. 4 logb x - logb y - 2 logb z
C. 2 logb x + 2 logb y + 2 logb z
D. logb x - logb y + 2 logb z
9) The exponential function f with base b is defined by f(x) = __________, b > 0 and b ≠ 1. Using interval notation, the domain of this function is __________ and the range is __________.
A. bx; (∞, -∞); (1, ∞)
B. bx; (-∞, -∞); (2, ∞)
C. bx; (-∞, ∞); (0, ∞)
D. bx; (-∞, -∞); (-1, ∞)
10) Approximate the following using a calculator; round your answer to three decimal places.
3√5
A. .765
B. 14297
C. 11.494
D. 11.665
11) Write the following equation in its equivalent exponential form.
4 = log2 16
A. 2 log4 = 16
B. 22 = 4
C. 44 = 256
D. 24 = 16
12) Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
31-x = 1/27
A. {2}
B. {-7}
C. {4}
D. {3}
13) Use properties of logarithms to expand the following logarithmic expression as much as possible.
logb (x2y)
A. 2 logy x + logx y
B. 2 logb x + logb y
C. logx - logb y
D. logb x – ...
Math 111 Final Exam Review1. Use the graph of y = f(x) in .docxandreecapon
Math 111 Final Exam Review
1. Use the graph of y = f(x) in Figure 1 to answer the following. Approximate where necessary.
(a) Evaluate f(−1).
(b) Evaluate f(0).
(c) Solve f(x) = 0.
(d) Solve f(x) = −7.
(e) Determine if f is even, odd, or neither from its
graph.
(f) State any local maximums or local minimums.
(g) State the domain and range of f.
(h) Over what interval(s) is the function increasing?
(i) Over what interval(s) is the function decreas-
ing?
(j) Over what interval(s) is the function concave
up?
(k) Over what interval(s) is the function concave
down?
(l) Find the zeros of f.
(m) Find a possible formula for this polynomial
function.
2
-2
-4
-6
2 4-2-4
x
y
Figure 1
2. Let f(x) =
2x − 1
x + 2
.
(a) Find f−1(x).
(b) Confirm the inverse by computing f−1 (f(x))
and f
(
f−1(x)
)
.
(c) State the domain and range of f and f−1.
(d) Evaluate f(0).
(e) Evaluate f−1(0).
(f) Solve f(x) = 3.
(g) Determine if f is even, odd, or neither from its
formula.
(h) State any horizontal and vertical asymptotes.
(i) State any horizontal and vertical intercepts.
(j) Sketch a graph of y = f(x) in Figure 2.
4
8
-4
-8
4 8-4-8
x
y
Figure 2
1
3. Let f(x) = |x|. For each of the following, sketch a graph of the tranformation in Figure 4 and
write the simplified formula for the function. Describe the order of transformations, being as specific
as possible and listing them in an appropriate order.
(a) −f(x)
(b) f(x + 1)
(c) 2f(x)
(d) f(x) + 3
(e) 2f(x + 1) + 3
(f) f(3x)
2
4
-2
-4
2 4-2-4
x
y
Figure 3. Graph of y = |x|
2
4
-2
-4
2 4-2-4
x
y
(a)
2
4
-2
-4
2 4-2-4
x
y
(b)
2
4
-2
-4
2 4-2-4
x
y
(c)
2
4
-2
-4
2 4-2-4
x
y
(d)
2
4
-2
-4
2 4-2-4
x
y
(e)
2
4
-2
-4
2 4-2-4
x
y
(f)
Figure 4
4. Complete Table 1 below using the given values in the table. If any value is undefined, write
“undefined.”
Table 1
x -2 -1 0 1 2
f(x) 2 1 0 1 2
g(x) 4 2 0 -2 -4
(g ◦ f)(x)
(g · f)(x)
f(x) + g(x)
f(x)
g(x)
g−1(x)
Page 2 of 5
5. Find a formula for the piecewise-defined func-
tion graphed in Figure 5 below.
f(x) =
1
2
3
-1
-2
-3
1 2 3-1-2-3
x
y
b
bc bc
b
Figure 5. Graph of y = f(x)
6. In Figure 6, graph the piecewise function de-
fined by
f(x) =
x2 − 4, −2 ≤ x < 0
2, 0 < x < 1
−1
2
x + 2, x ≥ 1
1
2
3
-1
-2
-3
1 2 3-1-2-3
x
y
Figure 6
7. The volume, V (in cubic centimeters) of a circular balloon of radius r (in centimeters) is given by
V = f(r) = 4
3
πr3. As someone blows air into the balloon, the radius of the balloon as a function of
time t (in seconds) is given by r = g(t) = 2t.
(a) Find and interpret f(3).
(b) Find and interpret g(3).
(c) Find and interpret f(g(3)).
(d) Find and interpret f(g(t)).
(e) Explain why g(f(r)) in nonsense.
(f) Find and interpret r = f−1(V ).
(g) Find and interpret f−1(20).
8. Write the following using exponents.
(a) log4 (64) = 3 (b) ln (
√
e) = 1
2
(c) log10
(
1
100
)
= −2
9. Solve the follow ...
Please be sure to save at least once every 15 minutes. If you leav.docxrandymartin91030
Please be sure to save at least once every 15 minutes. If you leave this page without saving, or if your session times out, any answers you have not saved will be lost. The Submit for Grading button will become available once you've answered all questions. Exams are not timed; you do not have to finish an exam in one sitting as long as you have saved your answers.
Q1. Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1.
a. -3
b. -2
c. 3
d. 2
Q2. Solve the inequality.
(x - 5)(x2 + x + 1) > 0
a. (-∞, -1) or (1, ∞)
b. (-1, 1)
c. (-∞, 5)
d. (5, ∞)
Q3. Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.
f(x) = 8x3 - 10x2 + 3x + 5; [-1, 0]
a. f(-1) = -16 and f(0) = -5; no
b. f(-1) = -16 and f(0) = 5; yes
c. f(-1) = 16 and f(0) = -5; yes
d. f(-1) = 16 and f(0) = 5; no
Q4. Solve the equation in the real number system.
x4 - 3x3 + 5x2 - x - 10 = 0
a. {-1, -2}
b. {1, 2}
c. {-1, 2}
d. {-2, 1}
Q5. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = x2 - 2x - 5
a. maximum; 1
b. minimum; 1
c. maximum; - 6
d. minimum; - 6
Q6. Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither.
f(x) = a. symmetry with respect to the origin
b. symmetry with respect to the y-axis
c. neither
Q7. Find the domain of the rational function.
f(x) = .
a. {x|x ≠ -3, x ≠ 5}
b. {x|x ≠ 3, x ≠ -5}
c. all real numbers
d. {x|x ≠ 3, x ≠ -3, x ≠ -5}
Q8. Find the domain of the rational function.
g(x) = a. all real numbers
b. {x|x ≠ -7, x ≠ 7, x ≠ -5}
c. {x|x ≠ -7, x ≠ 7}
d. {x|x ≠ 0, x ≠ -49}
Q9. Find all zeros of the function and write the polynomial as a product of linear factors.
f(x) = 3x4 + 4x3 + 13x2 + 16x + 4
a. f(x) = (3x - 1)(x - 1)(x + 2)(x - 2)
b. f(x) = (3x + 1)(x + 1)(x + 2i)(x - 2i)
c. f(x) = (3x - 1)(x - 1)(x + 2i)(x - 2i)
d. f(x) = (3x + 1)(x + 1)(x + 2)(x - 2)
Q10. Use the graph to find the vertical asymptotes, if any, of the function.
a. y = 0
b. x = 0, y = 0
c. x = 0
d. none
Q11. Find the power function that the graph of f resembles for large values of |x|.
f(x) = (x + 5)2
a. y = x10
b. y = x25
c. y = x2
d. y = x5
Q12. Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither.
f(x) = a. symmetry with respect to the y-axis
b. symmetry with respect to the origin
c. neither
Q13. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = -x2 - 2x + 2
a. minimum; - 1
b. maximum; 3
c. minimum; 3
d. maximum; - 1
Q14. Find the power function that the graph of f resembles for large values of |x|.
f(x) = -x2(x + 4)3(x2 - 1)
a. y = x7.
MATH 107 FINAL EXAMINATIONMULTIPLE CHOICE1. Deter.docxTatianaMajor22
MATH 107 FINAL EXAMINATION
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function.
A. Domain [–2, 2];
B. Domain [–1, 1];
C. Domain [–1, 3];
D. Domain [–3/2, –1/2];
2. Solve:
A. 3
B. 3,7
C. 9
D. No solution
3. Determine the interval(s) on which the function is increasing.
A. (−1.3, 1.3)
B. (1, 3)
C. (−∞,−1)and (3,∞)
D. (−2.5, 1)and (4.5,∞)
4. Determine whether the graph of y = 2|x| + 1 is symmetric with respect to the origin,
the x-axis, or the y-axis.
A. symmetric with respect to the origin only
B. symmetric with respect to the x-axis only
C. symmetric with respect to the y-axis only
D. not symmetric with respect to the origin, not symmetric with respect to the x-axis, and
not symmetric with respect to the y-axis
5. Solve, and express the answer in interval notation: | 9 – 7x | ≤ 12.
A. (–∞, –3/7]
B. (–∞, −3/7] ∪ [3, ∞) C. [–3, 3/7]
D. [–3/7, 3]
6. Which of the following represents the graph of 7x + 2y = 14 ?
A. B.
C. D.
7. Write a slope-intercept equation for a line parallel to the line x – 2y = 6 which passes through the point (10, – 4).
A.
B.
C.
D.
8. Which of the following best describes the graph?
A. It is the graph of a function and it is one-to-one.
B. It is the graph of a function and it is not one-to-one.
C. It is not the graph of a function and it is one-to-one.
D. It is not the graph of a function and it is not one-to-one.
9. Express as a single logarithm: log x + log 1 – 6 log (y + 4)
A.
B.
C.
D.
10. Which of the functions corresponds to the graph?
A.
B.
C.
D.
11. Suppose that a function f has exactly one x-intercept.
Which of the following statements MUST be true?
A. f is a linear function.
B. f (x) ≥ 0 for all x in the domain of f.
C. The equation f(x) = 0 has exactly one real-number solution.
D. f is an invertible function.
12. The graph of y = f(x) is shown at the left and the graph of y = g(x) is shown at the right. (No formulas are given.) What is the relationship between g(x) and f(x)?
y = f (x) y = g(x)
A. g(x) = f (x – 3) + 1
B. g(x) = f (x – 1) + 3
C. g(x) = f (x + 3) – 1
D. g(x) = f (x + 1) .
1. Write an equation in standard form of the parabola that has th.docxKiyokoSlagleis
1.
Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x
2
, but with the given point as the vertex (5, 3).
A. f(x) = (2x - 4) + 4
B. f(x) = 2(2x + 8) + 3
C. f(x) = 2(x - 5)
2
+ 3
D. f(x) = 2(x + 3)
2
+ 3
2 of 20
5.0 Points
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
f(x) = 2(x - 3)
2
+ 1
A. (3, 1)
B. (7, 2)
C. (6, 5)
D. (2, 1)
3 of 20
5.0 Points
Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.
g(x) = x + 3/x(x + 4)
A. Vertical asymptotes: x = 4, x = 0; holes at 3x
B. Vertical asymptotes: x = -8, x = 0; holes at x + 4
C. Vertical asymptotes: x = -4, x = 0; no holes
D. Vertical asymptotes: x = 5, x = 0; holes at x - 3
4 of 20
5.0 Points
"Y varies directly as the n
th
power of x" can be modeled by the equation:
A. y = kx
n
.
B. y = kx/n.
C. y = kx
*n
.
D. y = kn
x
.
5 of 20
5.0 Points
40 times a number added to the negative square of that number can be expressed as:
A.
A(x) = x
2
+ 20x.
B. A(x) = -x + 30x.
C.
A(x) = -x
2
- 60x.
D.
A(x) = -x
2
+ 40x.
6 of 20
5.0 Points
The graph of f(x) = -x
3
__________ to the left and __________ to the right.
A. rises; falls
B. falls; falls
C. falls; rises
D. falls; falls
Solve the following formula for the specified variable:
V = 1/3 lwh for h
7 of 20
Write an equation that expresses each relationship. Then solve the equation for y.
x varies jointly as y and z
A. x = kz; y = x/k
B. x = kyz; y = x/kz
C. x = kzy; y = x/z
D. x = ky/z; y = x/zk
8 of 20
8 times a number subtracted from the squared of that number can be expressed as:
A. P(x) = x + 7x.
B.P(x) = x
2
- 8x.
C. P(x) = x - x.
P(x) = x
2
+ 10x.
9of 20
Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.
f(x) = x
4
- 9x
2
A. x = 0, x = 3, x = -3; f(x) crosses the x-axis at -3 and 3; f(x) touches the x-axis at 0.
B. x = 1, x = 2, x = 3; f(x) crosses the x-axis at 2 and 3; f(x) crosses the x-axis at 0.
C. x = 0, x = -3, x = 5; f(x) touches the x-axis at -3 and 5; f(x) touches the x-axis at 0.
D. x = 1, x = 2, x = -4; f(x) crosses the x-axis at 2 and -4; f(x) touches the x-axis at 0.
10 of 20
Find the domain of the following rational function.
f(x) = x + 7/x
2
+ 49
A. All real numbers < 69
B. All real numbers > 210
C. All real numbers ≤ 77
D. All real numbers
11 of 20
Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x
2
or g(x) = -3x
2
, but with the given maximum or minimum.
Minimum = 0 at x = 11
A. f(x) = 6(x - 9)
B. f(x) = 3(x - 11)
2
C. f(x) = 4(x + 10)
D. f(x) = 3(x
2
- 15)
2
12 of 20
Solve the following polynomial inequality.
3x
2
+ 10x - 8 ≤ 0
A. [6, 1/3]
B. [-4, 2/3]
C. [-9, 4/5]
D. [8, 2/7]
13 of 20
Find the coordinate.
1) Use properties of logarithms to expand the following logarit.docxhirstcruz
1) Use properties of logarithms to expand the following logarithmic expression as much as possible.
Log
b
(√xy
3
/ z
3
)
A. 1/2 log
b
x - 6 log
b
y + 3 log
b
z
B. 1/2 log
b
x - 9 log
b
y - 3 log
b
z
C. 1/2 log
b
x + 3 log
b
y + 6 log
b
z
D. 1/2 log
b
x + 3 log
b
y - 3 log
b
z
2) Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution.
2 log x = log 25
A. {12}
B. {5}
C. {-3}
D. {25}
3) Write the following equation in its equivalent logarithmic form.
2
-4
= 1/16
A. Log
4
1/16 = 64
B. Log
2
1/24 = -4
C. Log
2
1/16 = -4
D. Log
4
1/16 = 54
4) Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.
log
2
96 – log
2
3
A. 5
B. 7
C. 12
D. 4
5) Use the exponential growth model, A = A
0
e
kt
, to show that the time it takes a population to double (to grow from A
0
to 2A
0
) is given by t = ln 2/k.
A. A
0
= A
0
e
kt
; ln = e
kt
; ln 2 = ln e
kt
; ln 2 = kt; ln 2/k = t
B. 2A
0
= A
0
e; 2= e
kt
; ln = ln e
kt
; ln 2 = kt; ln 2/k = t
C. 2A
0
= A
0
e
kt
; 2= e
kt
; ln 2 = ln e
kt
; ln 2 = kt; ln 2/k = t
D. 2A
0
= A
0
e
kt
; 2 = e
kt
; ln 1 = ln e
kt
; ln 2 = kt; ln 2/k = t
oe
6) Find the domain of following logarithmic function.
f(x) = log (2 - x)
A. (∞, 4)
B. (∞, -12)
C. (-∞, 2)
D. (-∞, -3)
7) An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e -0.000121t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in 5715 years?
A. Approximately 7 grams
B. Approximately 8 grams
C. Approximately 23 grams
D. Approximately 4 grams
8) Use properties of logarithms to expand the following logarithmic expression as much as possible.
log
b
(x
2
y) / z
2
A. 2 log
b
x + log
b
y - 2 log
b
z
B. 4 log
b
x - log
b
y - 2 log
b
z
C. 2 log
b
x + 2 log
b
y + 2 log
b
z
D. log
b
x - log
b
y + 2 log
b
z
9) The exponential function f with base b is defined by f(x) = __________, b > 0 and b ≠ 1. Using interval notation, the domain of this function is __________ and the range is __________.
A. bx; (∞, -∞); (1, ∞)
B. bx; (-∞, -∞); (2, ∞)
C. bx; (-∞, ∞); (0, ∞)
D. bx; (-∞, -∞); (-1, ∞)
10) Approximate the following using a calculator; round your answer to three decimal places.
3
√5
A. .765
B. 14297
C. 11.494
D. 11.665
11) Write the following equation in its equivalent exponential form.
4 = log
2
16
A. 2 log
4
= 16
B. 2
2
= 4
C. 4
4
= 256
D. 2
4
= 16
12) Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
3
1-x
= 1/27
A. {2}
B. {-7}
C. {4}
D. {3}
13) Use properties of logarithms to expand the followin.
1) Use properties of logarithms to expand the following logarithm.docxdorishigh
1) Use properties of logarithms to expand the following logarithmic expression as much as possible.
Logb (√xy3 / z3)
A. 1/2 logb x - 6 logb y + 3 logb z
B. 1/2 logb x - 9 logb y - 3 logb z
C. 1/2 logb x + 3 logb y + 6 logb z
D. 1/2 logb x + 3 logb y - 3 logb z
2) Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution.
2 log x = log 25
A. {12}
B. {5}
C. {-3}
D. {25}
3) Write the following equation in its equivalent logarithmic form.
2-4 = 1/16
A. Log4 1/16 = 64
B. Log2 1/24 = -4
C. Log2 1/16 = -4
D. Log4 1/16 = 54
4) Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.
log2 96 – log2 3
A. 5
B. 7
C. 12
D. 4
5) Use the exponential growth model, A = A0ekt, to show that the time it takes a population to double (to grow from A0 to 2A0 ) is given by t = ln 2/k.
A. A0 = A0ekt; ln = ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t
B. 2A0 = A0e; 2= ekt; ln = ln ekt; ln 2 = kt; ln 2/k = t
C. 2A0 = A0ekt; 2= ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t
D. 2A0 = A0ekt; 2 = ekt; ln 1 = ln ekt; ln 2 = kt; ln 2/k = toe
6) Find the domain of following logarithmic function.
f(x) = log (2 - x)
A. (∞, 4)
B. (∞, -12)
C. (-∞, 2)
D. (-∞, -3)
7) An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e -0.000121t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in 5715 years?
A. Approximately 7 grams
B. Approximately 8 grams
C. Approximately 23 grams
D. Approximately 4 grams
8) Use properties of logarithms to expand the following logarithmic expression as much as possible.
logb (x2 y) / z2
A. 2 logb x + logb y - 2 logb z
B. 4 logb x - logb y - 2 logb z
C. 2 logb x + 2 logb y + 2 logb z
D. logb x - logb y + 2 logb z
9) The exponential function f with base b is defined by f(x) = __________, b > 0 and b ≠ 1. Using interval notation, the domain of this function is __________ and the range is __________.
A. bx; (∞, -∞); (1, ∞)
B. bx; (-∞, -∞); (2, ∞)
C. bx; (-∞, ∞); (0, ∞)
D. bx; (-∞, -∞); (-1, ∞)
10) Approximate the following using a calculator; round your answer to three decimal places.
3√5
A. .765
B. 14297
C. 11.494
D. 11.665
11) Write the following equation in its equivalent exponential form.
4 = log2 16
A. 2 log4 = 16
B. 22 = 4
C. 44 = 256
D. 24 = 16
12) Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
31-x = 1/27
A. {2}
B. {-7}
C. {4}
D. {3}
13) Use properties of logarithms to expand the following logarithmic expression as much as possible.
logb (x2y)
A. 2 logy x + logx y
B. 2 logb x + logb y
C. logx - logb y
D. logb x – ...
Math 111 Final Exam Review1. Use the graph of y = f(x) in .docxandreecapon
Math 111 Final Exam Review
1. Use the graph of y = f(x) in Figure 1 to answer the following. Approximate where necessary.
(a) Evaluate f(−1).
(b) Evaluate f(0).
(c) Solve f(x) = 0.
(d) Solve f(x) = −7.
(e) Determine if f is even, odd, or neither from its
graph.
(f) State any local maximums or local minimums.
(g) State the domain and range of f.
(h) Over what interval(s) is the function increasing?
(i) Over what interval(s) is the function decreas-
ing?
(j) Over what interval(s) is the function concave
up?
(k) Over what interval(s) is the function concave
down?
(l) Find the zeros of f.
(m) Find a possible formula for this polynomial
function.
2
-2
-4
-6
2 4-2-4
x
y
Figure 1
2. Let f(x) =
2x − 1
x + 2
.
(a) Find f−1(x).
(b) Confirm the inverse by computing f−1 (f(x))
and f
(
f−1(x)
)
.
(c) State the domain and range of f and f−1.
(d) Evaluate f(0).
(e) Evaluate f−1(0).
(f) Solve f(x) = 3.
(g) Determine if f is even, odd, or neither from its
formula.
(h) State any horizontal and vertical asymptotes.
(i) State any horizontal and vertical intercepts.
(j) Sketch a graph of y = f(x) in Figure 2.
4
8
-4
-8
4 8-4-8
x
y
Figure 2
1
3. Let f(x) = |x|. For each of the following, sketch a graph of the tranformation in Figure 4 and
write the simplified formula for the function. Describe the order of transformations, being as specific
as possible and listing them in an appropriate order.
(a) −f(x)
(b) f(x + 1)
(c) 2f(x)
(d) f(x) + 3
(e) 2f(x + 1) + 3
(f) f(3x)
2
4
-2
-4
2 4-2-4
x
y
Figure 3. Graph of y = |x|
2
4
-2
-4
2 4-2-4
x
y
(a)
2
4
-2
-4
2 4-2-4
x
y
(b)
2
4
-2
-4
2 4-2-4
x
y
(c)
2
4
-2
-4
2 4-2-4
x
y
(d)
2
4
-2
-4
2 4-2-4
x
y
(e)
2
4
-2
-4
2 4-2-4
x
y
(f)
Figure 4
4. Complete Table 1 below using the given values in the table. If any value is undefined, write
“undefined.”
Table 1
x -2 -1 0 1 2
f(x) 2 1 0 1 2
g(x) 4 2 0 -2 -4
(g ◦ f)(x)
(g · f)(x)
f(x) + g(x)
f(x)
g(x)
g−1(x)
Page 2 of 5
5. Find a formula for the piecewise-defined func-
tion graphed in Figure 5 below.
f(x) =
1
2
3
-1
-2
-3
1 2 3-1-2-3
x
y
b
bc bc
b
Figure 5. Graph of y = f(x)
6. In Figure 6, graph the piecewise function de-
fined by
f(x) =
x2 − 4, −2 ≤ x < 0
2, 0 < x < 1
−1
2
x + 2, x ≥ 1
1
2
3
-1
-2
-3
1 2 3-1-2-3
x
y
Figure 6
7. The volume, V (in cubic centimeters) of a circular balloon of radius r (in centimeters) is given by
V = f(r) = 4
3
πr3. As someone blows air into the balloon, the radius of the balloon as a function of
time t (in seconds) is given by r = g(t) = 2t.
(a) Find and interpret f(3).
(b) Find and interpret g(3).
(c) Find and interpret f(g(3)).
(d) Find and interpret f(g(t)).
(e) Explain why g(f(r)) in nonsense.
(f) Find and interpret r = f−1(V ).
(g) Find and interpret f−1(20).
8. Write the following using exponents.
(a) log4 (64) = 3 (b) ln (
√
e) = 1
2
(c) log10
(
1
100
)
= −2
9. Solve the follow ...
Mid-Term Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Fill in the blank with one of the words or phrases listed below.
distributive real reciprocals absolute value opposite associative
inequality commutative whole algebraic expression exponent variable
1) The of a number is the distance between the number and 0 on the number line.
A) opposite B) whole
C) absolute value D) exponent
1)
Find an equation of the line. Write the equation using function notation.
2) Through (1, -3); perpendicular to f(x) = -4x - 3
A) f(x) =
1
4
x -
13
4
B) f(x) = -
1
4
x -
13
4
C) f(x) = -4x -
13
4
D) f(x) = 4x -
13
4
2)
Multiply or divide as indicated.
3)
60
-5
A) -22 B) 12 C) - 1
12
D) -12
3)
Write the sentence using mathematical symbols.
4) Two subtracted from x is 55.
A) 2 + x = 55 B) 2 - x = 55 C) x - 2 = 55 D) 55 - 2 = x
4)
Name the property illustrated by the statement.
5) (-10) + 10 = 0
A) associative property of addition B) additive identity property
C) commutative property of addition D) additive inverse property
5)
Tell whether the statement is true or false.
6) Every rational number is an integer.
A) True B) False
6)
Add or subtract as indicated.
7) -5 - 12
A) 7 B) -17 C) 17 D) -7
7)
1
Name the property illustrated by the statement.
8) (1 + 8) + 6 = 1 + (8 + 6)
A) distributive property
B) associative property of addition
C) commutative property of multiplication
D) associative property of multiplication
8)
Simplify the expression.
9) -(10v - 6) + 10(2v + 10)
A) 30v + 16 B) -10v + 94 C) 10v + 106 D) 30v + 4
9)
Solve the equation.
10) 5(x + 3) = 3[14 - 2(3 - x) + 10]
A) -39 B) 3 C) -13 D) 39
10)
List the elements of the set.
11) If A = {x|x is an odd integer} and B = {35, 37, 38, 40}, list the elements of A ∩ B.
A) {35, 37}
B) {x|x is an odd integer}
C) {x|x is an odd integer or x = 38 or x = 40}
D) { }
11)
Solve the inequality. Graph the solution set.
12) |x| ≥ 4
A) (-∞, -4] ∪ [4, ∞)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
B) [-4, 4]
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
C) [4, ∞)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
D) (-∞, -4) ∪ (4, ∞)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
12)
Solve.
13) The sum of three consecutive even integers is 336. Find the integers.
A) 108, 110, 112 B) 110, 112, 114 C) 112, 114, 116 D) 111, 112, 113
13)
2
Solve the inequality. Write your solution in interval notation.
14) x ≥ 4 or x ≥ -2
A) (-∞, ∞) B) [4, ∞)
C) [-2, ∞) D) (-∞, -2] ∪ [4, ∞)
14)
Use the formula A = P 1 + r
n
nt
to find the amount requested.
15) A principal of $12,000 is invested in an account paying an annual interest rate of 4%. Find the
amount in the account after 3 years if the account is compounded quarterly.
A) $1521.9 B) $13,388.02 C) $13,498.37 D) $13,521.90
15)
Graph the solution set ...
This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
Final Exam Name___________________________________Si.docxcharlottej5
Final Exam Name___________________________________
Silva Math 96 Spring 2020
YOU MUST SHOW ALL WORK AND BOX YOUR ANSWERS FOR CREDIT. WORK ALONE.
Solve the absolute value inequality. Write your answer
in interval notation.
1) |2x - 12 |> 2
Solve the compound inequality. Graph the solution set.
Write your answer in interval notation.
2) -4x > -8 and x + 4 > 3
Solve the three-part inequality. Write your answer in
interval notation.
3) -1 < 3x + 2 < 14
Solve the absolute value equation.
4) 4x + 9 = 2x + 7
Solve the compound inequality.
5) 3( x + 4 ) ≥ 0 or 4 ( x + 4 ) ≤ 4
Solve the inequality. Graph the solution set and write
your answer in interval notation.
6) |5k + 8| > -6
Solve the inequality graphically. Write your answer in
interval notation .
7) x + 3 ≥ 1
x-8 -6 -4 -2 2
y
8
6
4
2
x-8 -6 -4 -2 2
y
8
6
4
2
1
Graph the system of inequalities.
8) 2x + 8y ≥ -4
y < - 3
2
x + 6
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Find the determinant of the given matrix.
9) 10 5
0 -4
Use Cramer's rule to solve the system of linear
equations.
10) 6x + 5y = -12
2x - 2y = -4
Write a system that models the situation. Then solve the
system using any method. Must show work for credit.
11)A vendor sells hot dogs, bags of potato chips,
and soft drinks. A customer buys 3 hot dogs,
4 bags of potato chips, and 5 soft drinks for
$14.00. The price of a hot dog is $0.25 more
than the price of a bag of potato chips. The
cost of a soft drink is $1.25 less than the price
of two hot dogs. Find the cost of each item.
Use row reduced echelon form to solve the system.
12) x + y + z = 3
x - y + 4z = 11
5x + y + z = -9
2
Find the domain of f. Write your answer in interval
notation.
13) f(x) = 13 - 9x
If possible, simplify the expression. If any variables
exist, assume that they are positive.
14) 2x + 6 32x + 6 8x
Match to the equivalent expression.
15) 100-1/2
A) 1
1000
B) 1
10
C) 1
100
D) 1
10
Write the expression in standard form.
16) (5 + 8i) - (-3 + i)
Simplify the expression. Assume that all variables are
positive.
17) 5 t
5
z10
Solve the equation.
18) 3x + 1 = 3 + x - 4
Write the expression in standard form.
19) 3 + 3i
5 + 3i
3
Write the equation in vertex form.
20) y = x2 + 5x + 2
The graph of ax2 + bx + c is given. Use this graph to solve
ax2 + bx + c = 0, if possible.
21)
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
Solve the equation. Write complex solutions in standard
form.
22) 4x2 + 5x + 5 = 0
Graph the quadratic function by its properties.
23) f(x) = 1
3
x2 - 2x + 3
x
y
x
y
Solve the equation. Find all real solutions.
24) 2(x - 1)2 + 11(x - 1) + 12 = 0
Solve the problem.
25) The length of a table is 12 inches more than its
width. If the area of the table is 2668 square
inches, what is its length?
4
Solve the equation..
EVALUATING INTEGRALS.Evaluate the integral shown below. (H.docxgitagrimston
EVALUATING INTEGRALS.
Evaluate the integral shown below. (Hint: Try the substitution u = (7x2 + 3).)
1)
x dx
(7x2 + 3)5
Evaluate the integral shown below. (Hint: Apply a property of logarithms first.)
2)
ln x6
x
dx
1
Use the Fundamental Theorem of Calculus to find the derivative shown below.
3)
d
dx
x5
0
sin t dt
For the function shown below, sketch a graph of the function, and then find the SMALLEST possible value and the
LARGEST possible value for a Riemann sum of the function on the given interval as instructed.
4) f(x) = x2 ; between x = 3 and x = 7 with four rectangles of equal width.
^
CHARACTERISTICS and BEHAVIOR OF FUNCTIONS.
Use l'Hopital's rule to find the limit below.
5) lim
x
5x + 9
6x2 + 3x - 9
^
Use l'Hopital's rule to find the limit below. (Hint: The indeterminate form is f(x)g(x).)
6) lim
x
1 + 2
x3
x
2
Solve the following problem.
7) The 9 ft wall shown here stands 30 feet from the building. Find the length of the shortest straight beam that will
reach to the side of the building from the ground outside the wall.
9' wall
30'
Hint: Let "h" be the height on the building where the ladder touches; let "x" be the distance on the ground
between the wall and the foot of the ladder. Use similar triangles and the Pythagorean Theorem to write the
length of the beam "L" as a function of "x". Also note that a radical function is minimized when it radicand is
minimized.
For the function shown below, identify its local and absolute extreme values (if any), saying where they occur.
8) f(x) = -x3- 9x2 - 24x + 3
3
Find a value for "c" that satisfies the equation f(b) - f(a)
b - a
= f (c) in the conclusion of the Mean Value Theorem for the
function and interval shown below.
9) f(x) = x +
75
x
, on the interval [3, 25]
DERIVATIVES.
Find the equation of the tangent line to the curve whose function is shown below at the given point.
10) x5y5 = 32, tangent at (2, 1)
Use implicit differentiation to find dy/dx.
11) xy + x + y = x2y2
Given y = f(u) and u = g(x), find dy/dx = f (g(x))g (x).
12) y = u(u - 1), u = x2 + x
4
Find y .
13) y = (4x - 5)(4x3 - x2 + 1)
Find the derivative of the function "y" shown below.
14) y =
x2 + 8x + 3
x
Solve the problem below.
15) One airplane is approaching an airport from the north at 163 km/hr. A second airplane approaches from the east
at 261 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 31
km away from the airport and the westbound plane is 18 km from the airport.
FUNCTIONS, LIMITS and CONTINUITY.
Find the intervals on which the function shown below is continuous.
16) y =
x + 2
x2 - 8x + 7
5
A function f(x), a point c, the limit of f(x) as x approaches c, and a positive number is given. Find a number > 0 such
that for all x, 0 < x - c < f(x) - L < .
17) f(x) = 10x - 1, L = 29, c = 3, and = 0.01
Find all points "x" where the function shown below is discontinuous.
18)
Solve the "composite function ...
DirectionsUse what you have learned in this course to answer th.docxkimberly691
Directions:
Use what you have learned in this course to answer the following questions. Justify your responses completely. Each question is worth 5 points.
1.
Solve for
n
:
–6(
n
– 8) = 4(12 – 5
n
) + 14
n
.
2
. For
f(
x
) = 2|
x
+3| – 5
, name the type of function and describe each of the three transformations from the parent function
f(
x
) = |
x
|
.
3.
Determine whether
f
(
x
) = –5 – 10
x
+ 6
has a maximum or a minimum value. Find that value and explain how you know.
4.
The median weekly earnings for American workers in 1990 was $412 and in 1999 it was $549. Calculate the average rate of change between 1990 and 1999.
5.
Find the roots of the parabola given by the following equation.
2
x
2+ 5
x
- 9 = 2
x
6.
Describe the end behavior and determine whether the graph represents an odd-degree or an even-degree polynomial function. Then state the number of real zeros.
7.
GEOMETRY
Recall the formula for finding the area of a rectangle. Define a variable for the width and set up an equation to find the dimensions of a rectangle that has an area 144 square inches, given that the length is 10 inches longer than its width.
DIMENSIONS:
Length: Width:
8.
The amount
f
(
t
) of a certain medicine, in milligrams, in a patient’s bloodstream
t
minutes after being taken is given by
f
(
t
) =
.
Find the amount of medicine in the blood after 20 minutes.
9.
Graph
f(
x
) =
x
2 + 2
x
- 3
, label the function’s x-intercepts,
y
-intercept and vertex with their coordinates. Also draw in and label the axis of symmetry.
Image result for x y axis
10.
Determine whether the relation shown is a function. Explain how you know.
73-1.jpg
11.
Solve the inequality and graph the solution on a number line.
–3(5
y
– 4) ≥ 17
12.
Assume that the wooden triangle shown is a right triangle.
a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram.
Hint: (leg 1)2 + (leg 2)2 = (hypotenuse)2
b. Transform each side of the equation to determine if it is an identity.
13.
Use long division or synthetic division to find the quotient of .
14.
Simplify
(9 + 8 – 6)(4 – 5)
.
15.
Find the inverse of
h(
x
) = .
16.
If
f(
x
) = 2
x
– 1
and
g(
x
) = – 2
, find
[g
◦ f](
x
).
17.
Graph the function
y
= – 2
. Then state the domain and range of the function.
Domain:
Range:
18.
If
f(
x
) = 3
x
2 – 2
and
g(
x
) = 4x + 2
, what is the value of
f
+ g 2
?
The price of a sweatshirt at a local shop is twice the price of a pair of shorts. The price of a T-shirt at the shop is $4 less than the price of a pair of shorts. Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for a total cost of $136.
19.
Let
w
represent the price of one sweatshirt,
t
represent the price of one T-shirt, and
h
represent the price of one pair of shorts. Write a system of three equations that represents the prices of the clothing.
20.
Solve the system. Find the cost of eac.
APA, The assignment require a contemporary approach addressing Race,.docxamrit47
APA, The assignment require a contemporary approach addressing Race, Gender, and Crime. All work will include an introduction and a cogent thesis. The literature review will include a body of knowledge inclusive of in text citations, and supporting relevant references. The paper should end with discussions that highlight the future of the CJS. A conclusion of the literature review will end the written assignment. The assignment will consist of 2000 words. Reference page along with 6 peer reviewed references and course textbook.
.
APA style and all questions answered ( no min page requirements) .docxamrit47
APA style and all questions answered ( no min page requirements)
Diagnostic Techniques -
Pick any two diseases that require diagnostic tests to identify them from the body system. Use one of the body systems: cardiovascular, respiratory, renal, hepatobiliary, lymphatic, reproductive or nervous systems. For each of the diseases, explain:
Why is a particular test recommended?
How does the test work?
What information is obtained from the diagnostic test regarding the disease?
Does the diagnosis need confirmation with another diagnostic test?
.
More Related Content
Similar to Q1. Determine, without graphing, whether the given quadratic funct.docx
Mid-Term Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Fill in the blank with one of the words or phrases listed below.
distributive real reciprocals absolute value opposite associative
inequality commutative whole algebraic expression exponent variable
1) The of a number is the distance between the number and 0 on the number line.
A) opposite B) whole
C) absolute value D) exponent
1)
Find an equation of the line. Write the equation using function notation.
2) Through (1, -3); perpendicular to f(x) = -4x - 3
A) f(x) =
1
4
x -
13
4
B) f(x) = -
1
4
x -
13
4
C) f(x) = -4x -
13
4
D) f(x) = 4x -
13
4
2)
Multiply or divide as indicated.
3)
60
-5
A) -22 B) 12 C) - 1
12
D) -12
3)
Write the sentence using mathematical symbols.
4) Two subtracted from x is 55.
A) 2 + x = 55 B) 2 - x = 55 C) x - 2 = 55 D) 55 - 2 = x
4)
Name the property illustrated by the statement.
5) (-10) + 10 = 0
A) associative property of addition B) additive identity property
C) commutative property of addition D) additive inverse property
5)
Tell whether the statement is true or false.
6) Every rational number is an integer.
A) True B) False
6)
Add or subtract as indicated.
7) -5 - 12
A) 7 B) -17 C) 17 D) -7
7)
1
Name the property illustrated by the statement.
8) (1 + 8) + 6 = 1 + (8 + 6)
A) distributive property
B) associative property of addition
C) commutative property of multiplication
D) associative property of multiplication
8)
Simplify the expression.
9) -(10v - 6) + 10(2v + 10)
A) 30v + 16 B) -10v + 94 C) 10v + 106 D) 30v + 4
9)
Solve the equation.
10) 5(x + 3) = 3[14 - 2(3 - x) + 10]
A) -39 B) 3 C) -13 D) 39
10)
List the elements of the set.
11) If A = {x|x is an odd integer} and B = {35, 37, 38, 40}, list the elements of A ∩ B.
A) {35, 37}
B) {x|x is an odd integer}
C) {x|x is an odd integer or x = 38 or x = 40}
D) { }
11)
Solve the inequality. Graph the solution set.
12) |x| ≥ 4
A) (-∞, -4] ∪ [4, ∞)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
B) [-4, 4]
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
C) [4, ∞)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
D) (-∞, -4) ∪ (4, ∞)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
12)
Solve.
13) The sum of three consecutive even integers is 336. Find the integers.
A) 108, 110, 112 B) 110, 112, 114 C) 112, 114, 116 D) 111, 112, 113
13)
2
Solve the inequality. Write your solution in interval notation.
14) x ≥ 4 or x ≥ -2
A) (-∞, ∞) B) [4, ∞)
C) [-2, ∞) D) (-∞, -2] ∪ [4, ∞)
14)
Use the formula A = P 1 + r
n
nt
to find the amount requested.
15) A principal of $12,000 is invested in an account paying an annual interest rate of 4%. Find the
amount in the account after 3 years if the account is compounded quarterly.
A) $1521.9 B) $13,388.02 C) $13,498.37 D) $13,521.90
15)
Graph the solution set ...
This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
Final Exam Name___________________________________Si.docxcharlottej5
Final Exam Name___________________________________
Silva Math 96 Spring 2020
YOU MUST SHOW ALL WORK AND BOX YOUR ANSWERS FOR CREDIT. WORK ALONE.
Solve the absolute value inequality. Write your answer
in interval notation.
1) |2x - 12 |> 2
Solve the compound inequality. Graph the solution set.
Write your answer in interval notation.
2) -4x > -8 and x + 4 > 3
Solve the three-part inequality. Write your answer in
interval notation.
3) -1 < 3x + 2 < 14
Solve the absolute value equation.
4) 4x + 9 = 2x + 7
Solve the compound inequality.
5) 3( x + 4 ) ≥ 0 or 4 ( x + 4 ) ≤ 4
Solve the inequality. Graph the solution set and write
your answer in interval notation.
6) |5k + 8| > -6
Solve the inequality graphically. Write your answer in
interval notation .
7) x + 3 ≥ 1
x-8 -6 -4 -2 2
y
8
6
4
2
x-8 -6 -4 -2 2
y
8
6
4
2
1
Graph the system of inequalities.
8) 2x + 8y ≥ -4
y < - 3
2
x + 6
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Find the determinant of the given matrix.
9) 10 5
0 -4
Use Cramer's rule to solve the system of linear
equations.
10) 6x + 5y = -12
2x - 2y = -4
Write a system that models the situation. Then solve the
system using any method. Must show work for credit.
11)A vendor sells hot dogs, bags of potato chips,
and soft drinks. A customer buys 3 hot dogs,
4 bags of potato chips, and 5 soft drinks for
$14.00. The price of a hot dog is $0.25 more
than the price of a bag of potato chips. The
cost of a soft drink is $1.25 less than the price
of two hot dogs. Find the cost of each item.
Use row reduced echelon form to solve the system.
12) x + y + z = 3
x - y + 4z = 11
5x + y + z = -9
2
Find the domain of f. Write your answer in interval
notation.
13) f(x) = 13 - 9x
If possible, simplify the expression. If any variables
exist, assume that they are positive.
14) 2x + 6 32x + 6 8x
Match to the equivalent expression.
15) 100-1/2
A) 1
1000
B) 1
10
C) 1
100
D) 1
10
Write the expression in standard form.
16) (5 + 8i) - (-3 + i)
Simplify the expression. Assume that all variables are
positive.
17) 5 t
5
z10
Solve the equation.
18) 3x + 1 = 3 + x - 4
Write the expression in standard form.
19) 3 + 3i
5 + 3i
3
Write the equation in vertex form.
20) y = x2 + 5x + 2
The graph of ax2 + bx + c is given. Use this graph to solve
ax2 + bx + c = 0, if possible.
21)
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
Solve the equation. Write complex solutions in standard
form.
22) 4x2 + 5x + 5 = 0
Graph the quadratic function by its properties.
23) f(x) = 1
3
x2 - 2x + 3
x
y
x
y
Solve the equation. Find all real solutions.
24) 2(x - 1)2 + 11(x - 1) + 12 = 0
Solve the problem.
25) The length of a table is 12 inches more than its
width. If the area of the table is 2668 square
inches, what is its length?
4
Solve the equation..
EVALUATING INTEGRALS.Evaluate the integral shown below. (H.docxgitagrimston
EVALUATING INTEGRALS.
Evaluate the integral shown below. (Hint: Try the substitution u = (7x2 + 3).)
1)
x dx
(7x2 + 3)5
Evaluate the integral shown below. (Hint: Apply a property of logarithms first.)
2)
ln x6
x
dx
1
Use the Fundamental Theorem of Calculus to find the derivative shown below.
3)
d
dx
x5
0
sin t dt
For the function shown below, sketch a graph of the function, and then find the SMALLEST possible value and the
LARGEST possible value for a Riemann sum of the function on the given interval as instructed.
4) f(x) = x2 ; between x = 3 and x = 7 with four rectangles of equal width.
^
CHARACTERISTICS and BEHAVIOR OF FUNCTIONS.
Use l'Hopital's rule to find the limit below.
5) lim
x
5x + 9
6x2 + 3x - 9
^
Use l'Hopital's rule to find the limit below. (Hint: The indeterminate form is f(x)g(x).)
6) lim
x
1 + 2
x3
x
2
Solve the following problem.
7) The 9 ft wall shown here stands 30 feet from the building. Find the length of the shortest straight beam that will
reach to the side of the building from the ground outside the wall.
9' wall
30'
Hint: Let "h" be the height on the building where the ladder touches; let "x" be the distance on the ground
between the wall and the foot of the ladder. Use similar triangles and the Pythagorean Theorem to write the
length of the beam "L" as a function of "x". Also note that a radical function is minimized when it radicand is
minimized.
For the function shown below, identify its local and absolute extreme values (if any), saying where they occur.
8) f(x) = -x3- 9x2 - 24x + 3
3
Find a value for "c" that satisfies the equation f(b) - f(a)
b - a
= f (c) in the conclusion of the Mean Value Theorem for the
function and interval shown below.
9) f(x) = x +
75
x
, on the interval [3, 25]
DERIVATIVES.
Find the equation of the tangent line to the curve whose function is shown below at the given point.
10) x5y5 = 32, tangent at (2, 1)
Use implicit differentiation to find dy/dx.
11) xy + x + y = x2y2
Given y = f(u) and u = g(x), find dy/dx = f (g(x))g (x).
12) y = u(u - 1), u = x2 + x
4
Find y .
13) y = (4x - 5)(4x3 - x2 + 1)
Find the derivative of the function "y" shown below.
14) y =
x2 + 8x + 3
x
Solve the problem below.
15) One airplane is approaching an airport from the north at 163 km/hr. A second airplane approaches from the east
at 261 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 31
km away from the airport and the westbound plane is 18 km from the airport.
FUNCTIONS, LIMITS and CONTINUITY.
Find the intervals on which the function shown below is continuous.
16) y =
x + 2
x2 - 8x + 7
5
A function f(x), a point c, the limit of f(x) as x approaches c, and a positive number is given. Find a number > 0 such
that for all x, 0 < x - c < f(x) - L < .
17) f(x) = 10x - 1, L = 29, c = 3, and = 0.01
Find all points "x" where the function shown below is discontinuous.
18)
Solve the "composite function ...
DirectionsUse what you have learned in this course to answer th.docxkimberly691
Directions:
Use what you have learned in this course to answer the following questions. Justify your responses completely. Each question is worth 5 points.
1.
Solve for
n
:
–6(
n
– 8) = 4(12 – 5
n
) + 14
n
.
2
. For
f(
x
) = 2|
x
+3| – 5
, name the type of function and describe each of the three transformations from the parent function
f(
x
) = |
x
|
.
3.
Determine whether
f
(
x
) = –5 – 10
x
+ 6
has a maximum or a minimum value. Find that value and explain how you know.
4.
The median weekly earnings for American workers in 1990 was $412 and in 1999 it was $549. Calculate the average rate of change between 1990 and 1999.
5.
Find the roots of the parabola given by the following equation.
2
x
2+ 5
x
- 9 = 2
x
6.
Describe the end behavior and determine whether the graph represents an odd-degree or an even-degree polynomial function. Then state the number of real zeros.
7.
GEOMETRY
Recall the formula for finding the area of a rectangle. Define a variable for the width and set up an equation to find the dimensions of a rectangle that has an area 144 square inches, given that the length is 10 inches longer than its width.
DIMENSIONS:
Length: Width:
8.
The amount
f
(
t
) of a certain medicine, in milligrams, in a patient’s bloodstream
t
minutes after being taken is given by
f
(
t
) =
.
Find the amount of medicine in the blood after 20 minutes.
9.
Graph
f(
x
) =
x
2 + 2
x
- 3
, label the function’s x-intercepts,
y
-intercept and vertex with their coordinates. Also draw in and label the axis of symmetry.
Image result for x y axis
10.
Determine whether the relation shown is a function. Explain how you know.
73-1.jpg
11.
Solve the inequality and graph the solution on a number line.
–3(5
y
– 4) ≥ 17
12.
Assume that the wooden triangle shown is a right triangle.
a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram.
Hint: (leg 1)2 + (leg 2)2 = (hypotenuse)2
b. Transform each side of the equation to determine if it is an identity.
13.
Use long division or synthetic division to find the quotient of .
14.
Simplify
(9 + 8 – 6)(4 – 5)
.
15.
Find the inverse of
h(
x
) = .
16.
If
f(
x
) = 2
x
– 1
and
g(
x
) = – 2
, find
[g
◦ f](
x
).
17.
Graph the function
y
= – 2
. Then state the domain and range of the function.
Domain:
Range:
18.
If
f(
x
) = 3
x
2 – 2
and
g(
x
) = 4x + 2
, what is the value of
f
+ g 2
?
The price of a sweatshirt at a local shop is twice the price of a pair of shorts. The price of a T-shirt at the shop is $4 less than the price of a pair of shorts. Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for a total cost of $136.
19.
Let
w
represent the price of one sweatshirt,
t
represent the price of one T-shirt, and
h
represent the price of one pair of shorts. Write a system of three equations that represents the prices of the clothing.
20.
Solve the system. Find the cost of eac.
APA, The assignment require a contemporary approach addressing Race,.docxamrit47
APA, The assignment require a contemporary approach addressing Race, Gender, and Crime. All work will include an introduction and a cogent thesis. The literature review will include a body of knowledge inclusive of in text citations, and supporting relevant references. The paper should end with discussions that highlight the future of the CJS. A conclusion of the literature review will end the written assignment. The assignment will consist of 2000 words. Reference page along with 6 peer reviewed references and course textbook.
.
APA style and all questions answered ( no min page requirements) .docxamrit47
APA style and all questions answered ( no min page requirements)
Diagnostic Techniques -
Pick any two diseases that require diagnostic tests to identify them from the body system. Use one of the body systems: cardiovascular, respiratory, renal, hepatobiliary, lymphatic, reproductive or nervous systems. For each of the diseases, explain:
Why is a particular test recommended?
How does the test work?
What information is obtained from the diagnostic test regarding the disease?
Does the diagnosis need confirmation with another diagnostic test?
.
Apa format1-2 paragraphsreferences It is often said th.docxamrit47
Apa format
1-2 paragraphs
references
It is often said that people today are no longer loyal to organizations. Yet employees are loyal to their direct supervisor. This discussion question asks you to evaluate and apply your understanding of followership theory. Reflect on any techniques for understanding, achieving, and positively applying organizational and personal power and influence as a follower.
When effective leaders leave an organization to move on to another organization, they often take at least one or two employees. Employees who respect a leader and have generated a relationship and bond want to work under that leader. One indicator of effective leaders is communication skills in which a leader is attuned to the needs of each employee.
REAL-LIFE APPLICATION: Discuss a leader with whom you are familiar and who has the loyalty of his or her direct reports. Alternatively, you might interview a friend or family member about their experiences or you may research a well-known leader. Address the following in your response.
Evaluate how this leader earns respect and loyalty from his or her employees.
If you were in a leadership position, what methods would you implement to inspire, motivate, and empower your employees?
Support your discussion with at least one scholarly article and, if relevant, credible media reports, and cite each source using APA style.
.
APA format2-3 pages, double-spaced1. Choose a speech to review. It.docxamrit47
APA format2-3 pages, double-spaced
1. Choose a speech to review. It can be any type (informative, persuasive, special occasion). It should be between 7-20 minutes. You may search Youtube for videos of speeches (TED talks, commencement speeches, public addresses by government etc).
Copy the link of the video you've chosen to your submission form.
2. Analyze the speech content and speaker delivery, paying attention to:
what the message is
how the message is organized
nonverbal cues (tone, pitch, pauses, gestures etc)
the context in which the message is being delivered
3. Provide your opinion on the speech and speaker delivery.
What do you think the intention of the speaker is?
Does the effect on the audience seem to follow that intention?
What did you like about the speech?
Is it appropriate for the context; why?
Be sure to attach your essay as a .doc or .rtf file and make sure to proofread for spelling and grammar errors.
.
APA format httpsapastyle.apa.orghttpsowl.purd.docxamrit47
APA format
https://apastyle.apa.org/
https://owl.purdue.edu/owl/research_and_citation/apa_style/apa_formatting_and_style_guide/general_format.html
Min number of pages are 30 pages
Must have
Contents with page numbers
Abstract
Introduction
The problem
Are there any sub-problems?
Is there any issue need to be present in relation to the problem?
The solutions
Steps of the solutions
Compare the solution to other solution
Any suggestion to improve the solution
Conclusion
References
Research Paper topic:
Computer Security Objects Register
https://csrc.nist.gov/Projects/Computer-Security-Objects-Register
The Computer Security Objects Register (CSOR) specifies names that uniquely identify CSOs. These unique names are used to reference these objects in abstract specifications and during the negotiation of security services for a transaction or application.
The studies must look at different algorithms used CSOR and the benefits of using CSOR
.
APA format2-3 pages, double-spaced1. Choose a speech to review. .docxamrit47
APA format2-3 pages, double-spaced
1. Choose a speech to review. It can be any type (informative, persuasive, special occasion). It should be between 7-20 minutes. You may search Youtube for videos of speeches (TED talks, commencement speeches, public addresses by government etc).
Copy the link of the video you've chosen to your submission form.
2. Analyze the speech content and speaker delivery, paying attention to:
what the message is
how the message is organized
nonverbal cues (tone, pitch, pauses, gestures etc)
the context in which the message is being delivered
3. Provide your opinion on the speech and speaker delivery.
What do you think the intention of the speaker is?
Does the effect on the audience seem to follow that intention?
What did you like about the speech?
Is it appropriate for the context; why?
Be sure to attach your essay as a .doc or .rtf file and make sure to proofread for spelling and grammar errors.
.
APA Formatting AssignmentUse the information below to create.docxamrit47
APA Formatting Assignment
Use the information below to create a reference list using proper APA formatting
1)
Authors: Christina Jane Jones, Helen Smith and Carrie Llewellyn
Title: Evaluating the effectiveness of health belief model interventions in improving adherence: a
systematic review
Publication Year: 2014
Journal: Health Psychology Review, Vol. 8, No. 3, 253_269
DOI: 10.1080/17437199.2013.802623
2)
Authors: Mohammad Bagherniya, Ali Taghipour, Manoj Sharma, Amirhossein Sahebkar, Isobel R.
Contento, Seyed Ali Keshavarz, Firoozeh Mostafavi Darani and Mohammad Safarian
Title: Obesity intervention programs among adolescents using social cognitive theory: a systematic
literature review
Publication Year: 2018
Journal: Health Education Research, Vol. 33, No. 1, 26_39
3)
Authors: Christine Y. K. Lau, Kris Y. W. Lok, Marie Tarrant
Title: Breastfeeding Duration and the Theory of Planned Behavior and Breastfeeding Self-Efficacy
Framework: A Systematic Review of Observational Studies
Publication Year: 2018
Journal: Maternal and Child Health Journal, Vol. 22, 327_342
DOI: 10.1007/s10995-018-2453-x
4)
Authors: Amy E. Bodde, Dong-Chul Seo
Title: A review of social and environmental barriers to physical activity for adults with intellectual
disabilities
Publication Year: 2009
Journal: Disability and Health Journal, Vol. 2, 57_66
5)
Authors: Linda Irvine, Ambrose J. Melson, Brian Williams, Falko F. Sniehotta, Gerry Humphris, Iain K.
Crombie
Title: Design and development of a complex narrative intervention delivered by text messages to reduce
binge drinking among socially disadvantaged men
Publication Year: 2018
Journal: Pilot and Feasibility Studies, Vol. 4, No.105, 1_11
.
APA style300 words10 maximum plagiarism Mrs. Smith was.docxamrit47
APA style
300 words
10% maximum plagiarism
Mrs. Smith was a 73-year-old widow who lived alone with no significant social support. She had been suffering from emphysema for several years and had had frequent hospitalizations for respiratory problems. On the last hospital admission, her pneumonia quickly progressed to organ failure. Death appeared to be imminent, and she went in and out of consciousness, alone in her hospital room. The medical-surgical nursing staff and the nurse manager focused on making Mrs. Smith’s end-of-life period as comfortable as possible. Upon consultation with the vice president for nursing, the nurse manager and the unit staff nurses decided against moving Mrs. Smith to the palliative care unit, although considered more economical, because of the need to protect and nurture her because she was already experiencing signs and symptoms of the dying process. Nurses were prompted by an article they read on human caring as the “language of nursing practice” (Turkel, Ray, & Kornblatt, 2012) in their weekly caring practice meetings.
The nurse manager reorganized patient assignments. She felt that the newly assigned clinical nurse leader who was working between both the medical and surgical units could provide direct nurse caring and coordination at the point of care (Sherman, 2012). Over the next few hours, the clinical nurse leader and a staff member who had volunteered her assistance provided personal care for Mrs. Smith. The clinical nurse leader asked the nurse manager whether there was a possibility that Mrs. Smith had any close friends who could “be there” for her in her final moments. One friend was discovered and came to say goodbye to Mrs. Smith. With help from her team, the clinical nurse leader turned, bathed, and suctioned Mrs. Smith. She spoke quietly, prayed, and sang hymns softly in Mrs. Smith’s room, creating a peaceful environment that expressed compassion and a deep sense of caring for her. The nurse manager and nursing unit staff were calmed and their “hearts awakened” by the personal caring that the clinical nurse leader and the volunteer nurse provided. Mrs. Smith died with caring persons at her bedside, and all members of the unit staff felt comforted that she had not died alone.
Davidson, Ray, and Turkel (2011) note that caring is complex, and caring science includes the art of practice, “an aesthetic which illuminates the beauty of the dynamic nurse-patient relationship, that makes possible authentic spiritual-ethical choices for transformation—healing, health, well-being, and a peaceful death” (p. xxiv). As the clinical nurse leader and the nursing staff in this situation engaged in caring practice that focused on the well-being of the patient, they simultaneously created a caring-healing environment that contributed to the well-being of the whole—the emotional atmosphere of the unit, the ability of the clinical nurse leader and staff nurses to practice caringly and competently, and the qualit.
APA format1. What are the three most important takeawayslessons.docxamrit47
APA FORMAT
1. What are the three most important takeaways/lessons from the material provided in this module? (150 words or more)
2. Drawing on the material that was provided what else would like to know? What other related questions/ideas/topics would you like to explore in the future? (100 words or more)
3. What is lobbying? What role does it play in the relationship between government and business? (100 words or more)
.
APA General Format Summary APA (American Psychological.docxamrit47
APA General Format
Summary
APA (American Psychological Association) style is most commonly used to cite sources within
the social sciences. This resource, revised according to the 6th edition, second printing of the
APA manual, offers examples for the general format of APA research papers, in-text citations,
endnotes/footnotes, and the reference page. For more information, please consult the Publication
Manual of the American Psychological Association, (6th ed., 2nd printing).
Contributors: Joshua M. Paiz, Elizabeth Angeli, Jodi Wagner, Elena Lawrick, Kristen Moore,
Michael Anderson, Lars Soderlund, Allen Brizee, Russell Keck
Last Edited: 2016-05-13 12:06:24
Please use the example at the bottom of this page to cite the Purdue OWL in APA.
To see a side-by-side comparison of the three most widely used citation styles, including a chart
of all APA citation guidelines, see the Citation Style Chart.
You can also watch our APA vidcast series on the Purdue OWL YouTube Channel.
General APA Guidelines
Your essay should be typed, double-spaced on standard-sized paper (8.5" x 11") with 1" margins
on all sides. You should use a clear font that is highly readable. APA recommends using 12 pt.
Times New Roman font.
Include a page header (also known as the "running head") at the top of every page. To create
a page header/running head, insert page numbers flush right. Then type "TITLE OF YOUR
PAPER" in the header flush left using all capital letters. The running head is a shortened
version of your paper's title and cannot exceed 50 characters including spacing and punctuation.
Major Paper Sections
Your essay should include four major sections: The Title Page, Abstract, Main Body,
and References.
Title Page
The title page should contain the title of the paper, the author's name, and the institutional
affiliation. Include the page header (described above) flush left with the page number flush right
at the top of the page. Please note that on the title page, your page header/running head should
look like this:
Running head: TITLE OF YOUR PAPER
Pages after the title page should have a running head that looks like this:
TITLE OF YOUR PAPER
http://owl.english.purdue.edu/owl/resource/949/01/
http://www.youtube.com/playlist?list=PL8F43A67F38DE3D5D&feature=edit_ok
http://www.youtube.com/user/OWLPurdue
After consulting with publication specialists at the APA, OWL staff learned that the APA 6th
edition, first printing sample papers have incorrect examples of Running heads on pages after
the title page. This link will take you to the APA site where you can find a complete list of all the
errors in the APA's 6th edition style guide.
Type your title in upper and lowercase letters centered in the upper half of the page. APA
recommends that your title be no more than 12 words in length and that it should not contain
abbreviations or words that serve no purpose. Your title may take up one or two l.
Appearance When I watched the video of myself, I felt that my b.docxamrit47
Appearance
When I watched the video of myself, I felt that my black straight skirt, closed toed shoes and white collared shirt gave a professional appearance and more credibility with the audience. My hair was a little too casual. I wished I had that one strand tacked back so it would have stayed out of my eyes. This made it hard for the audience to see my face and was distracting when I had to keep tucking it back. My earrings were small so the audience would watch me and not my jewelry. I wasn’t standing up straight and it made me look less confident. I need to remember to have better posture when speaking.Organizational Pattern
My introduction was slow and clear and the story was suspenseful enough to grab their attention. It was a little confusing at the beginning because I didn’t preview the main points but because I transitioned well between the steps by saying, “Now that you have completed step 1, selecting the pattern, you are ready to move to step two, preparing the wood” the audience was able to follow. I remembered to state my research source for two of the steps but forgot the third. It made the third step seem shallower and I think I lost credibility. My word choice was good. I made sure to use a variety of descriptive words for the types of wood, explained new vocabulary and repeated phrases to help the audience remember the steps. For some reason the ending was weak. I didn’t tie it to the introduction or have a good ending sentence. It would have been a good idea to remind them of the beginning story and how woodworking affects their everyday life.Vocal Qualities
During my speech I had such a dry mouth that I messed up on the pronunciation of some of the words like saying “exspecially” instead of “especially.” This sounded less professional to the audience. I had good projection so that even the back row could hear without straining. My pitch variation is getting better but I still keep using the same rhythm with my pauses. This make me sound more monotone, like I’m reading the speech rather than just having a conversation. I’ll need to practice changing my rate and pauses. I also noticed many of my sentences end in an up-pitch, like I’m asking a question. If I bring some of those down it will make me appear more confident rather than questioning. It is hard to get rid of those filler words. “Like” and “so” are two of my favorites but it does make me sound like a teenager. I had no idea I said them so much.Delivery
There weren’t many gestures, which made me look stiff and nervous. I just held my note cards and stood in one spot the whole time. I need to do more with my hands and maybe move a little more in the space. I really admire the people in class who have such a good flow with their delivery from gestures to using the space around them purposefully. I felt I held my note cards too close to my face and had my head down most of the time. While watching the video, I noticed I looked at my cards and the poster a l.
apa format1-2 paragraphsreferencesFor this week’s .docxamrit47
apa format
1-2 paragraphs
references
For this week’s discussion, choose a current social movement from anywhere in the world. Then, using the required readings, videos, and your own research, discuss the “role these leaders” play in your chosen social movement. In addition, describe any group or collective processes that you discovered. Use specific examples to make major points.
Support your writing with at least two scholarly sources that are
in addition
to required reading.
.
APA Format, with 2 references for each question and an assignment..docxamrit47
APA Format, with 2 references for each question and an assignment.
1. Some say that analytics in general dehumanize managerial
activities, and others say they do not. Discuss arguments
for both points of view.
3. What are some of the major privacy concerns in employing
intelligent systems on mobile data?
4. Identify some cases of violations of user privacy from
current literature and their impact on data science as a
profession.
Ex.2. Search the Internet to find examples of how intelligent
systems can facilitate activities such as empowerment,
mass customization, and teamwork.
Reflective Assignment:
What has been significant about this course that will help you perform data science tasks in the future.
.
APA-formatted 8-10 page research paper which examines the potential .docxamrit47
APA-formatted 8-10 page research paper which examines the potential psychological impact of long-term exposure to mass media messages on the major issues surrounding political advertising and political campaigns in the United States and why it is currently relevant and impacts society.
12 Point Times New Roman Font
Double Spaced
Please include research that supports ideas and topics related to political advertising and political campaigns in the United States.
.
APA STYLE 1.Define the terms multiple disabilities and .docxamrit47
APA STYLE
1.Define the terms
multiple disabilities
and
deaf-blindness
as described in the Individuals with Disabilities Act (IDEA)
2.Identify three types of educational assessments for students with severe and multiple disabilities.
3.Identify the features of effective services and supports for children with severe and multiple disabilities during a) early childhood years and b) elementary school years.
4. Distinguish between the term
deaf
and
hard of hearing
5.
Identify 4 approaches to teaching communication skills to people with a hearing loss.
6.
What are the distinctive features of refractive eye problems, muscle disorders of the eye and receptive eye problems?
7.Describe two content areas that should be included in educational programs for students with vision loss.
8. Identify several disabilities that may accompany cerebral palsy.
9.What is spina bifida myelomeningocele?
10.Describe the physical limitations associated with muscular distrophy
11.Describe the AIDS disease stages through which individuals with the syndrome move
12.Identify present and future interventions for the treatment of children and youth with cystic fibrosis.
.
APA STYLE follow this textbook answer should be summarize for t.docxamrit47
APA STYLE
follow this textbook answer should be summarize for this below text
Study all types of Distributive Justice (6 or 7 total)
Summarize each in
one sentence
. Produce examples for each.
Don't use
any other text or article except this one.
There are different theories of how to make the basic distribution. Among them are:
1. Scope and Role of Distributive Principles
2. Strict Egalitarianism
3. The Difference Principle
4. Equality of Opportunity and Luck Egalitarianism
5. Welfare-Based Principles
6. Desert-Based Principles
7. Libertarian Principles
8. Feminist Principles
There are different theories of how to make the basic distribution. Among them are:
Strict Egalitarianism
One of the simplest principles of distributive justice is that of strict, or radical, equality. The principle says that every person should have the same level of material goods and services. The principle is most commonly justified on the grounds that people are morally equal and that equality in material goods and services is the best way to give effect to this moral ideal.
The Difference Principle
The most widely discussed theory of distributive justice in the past four decades has been that proposed by John Rawls in
A Theory of Justice
, (Rawls 1971), and
Political Liberalism
, (Rawls 1993). Rawls proposes the following two principles of justice:
· 1. Each person has an equal claim to a fully adequate scheme of equal basic rights and liberties, which scheme is compatible with the same scheme for all; and in this scheme the equal political liberties, and only those liberties, are to be guaranteed their fair value.
· 2. Social and economic inequalities are to satisfy two conditions: (a) They are to be attached to positions and offices open to all under conditions of fair equality of opportunity; and (b), they are to be to the greatest benefit of the least advantaged members of society. (Rawls 1993, pp. 5–6. The principles are numbered as they were in Rawls' original
A Theory of Justice
.)
Equality of Opportunity and Luck Egalitarianism
Dworkin proposed that people begin with equal resources but be allowed to end up with unequal economic benefits as a result of their own choices. What constitutes a just material distribution is to be determined by the result of a thought experiment designed to model fair distribution. Suppose that everyone is given the same purchasing power and each uses that purchasing power to bid, in a fair auction, for resources best suited to their life plans. They are then permitted to use those resources as they see fit. Although people may end up with different economic benefits, none of them is given less consideration than another in the sense that if they wanted somebody else's resource bundle they could have bid for it instead.
In Dworkin's proposal we see his attitudes to ‘ambitions’ and ‘endowments’ which have become a central feature of luck egalitarianism (though under a wide variety of al.
APA7Page length 3-4, including Title Page and Reference Pag.docxamrit47
APA7
Page length: 3-4, including Title Page and Reference Page.
Discuss and explore the synergy that RFID technology & Time Based Competition has had on the grocery retail industry. Are the two concepts compatible? And then explain. Provide real-world scenarios, which reflect Time Base Competition.
video on
RFID in Logistics
.
APA format, 2 pagesThree general sections 1. an article s.docxamrit47
APA format, 2 pages
Three general sections:
1. an article summary,
2. how the article is relevant to psychology and human behavior (what do the results mean)
3. reaction to the article (was it interesting , were the results surprising, did it seem like common sense, etc.)
.
APA Style with minimum of 450 words, with annotations, quotation.docxamrit47
APA Style with minimum of 450 words, with annotations, quotations and 3 references.
. Mass vaccination after a disaster:
There was a natural disaster that occurred and has led to an infectious disease outbreak (your choice of one that is vaccine-preventable). Those affected by the disaster are settled in temporary locations with high population densities, inadequate food and shelter, unsafe water, poor sanitation and infrastructure that has been compromised or destroyed. There is a vaccine available for the infectious disease but there are not enough doses to give to all who are at-risk due to the natural disaster.
You are the public health official in charge of infectious disease prevention. Devise a plan to administer the vaccine to the population. Will you use a lottery system or target specific sub-populations? How will you track and monitor those who are vaccinated? Use the attributes of the infectious disease to provide reasoning behind your plan. What other prevention techniques that can be used to supplement the vaccination plan?
.
APA FORMAT1. What are the three most important takeawayslesson.docxamrit47
APA FORMAT
1. What are the three most important takeaways/lessons from the material provided in this online course (the entire quarter) and why? (150 words or more)
2. How did the material provided in this course assist your growth as a student and as an individual, in general? (150 words or more).
.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Q1. Determine, without graphing, whether the given quadratic funct.docx
1. Q1. Determine, without graphing, whether the given quadratic
function has a maximum value or a minimum value and then
find that value.
f(x) = x2 - 2x - 5
a. maximum; 1
b. minimum; 1
c. maximum; - 6
d. minimum; - 6
Q2. Find the domain of the rational function.
g(x) =
a. all real numbers
b. {x|x ≠ -7, x ≠ 7, x ≠ -5}
c. {x|x ≠ -7, x ≠ 7}
d. {x|x ≠ 0, x ≠ -49}
Q3. Solve the inequality.
(x - 5)(x2 + x + 1) > 0
a. (-∞, -1) or (1, ∞)
b. (-1, 1)
c. (-∞, 5)
d. (5, ∞)
Q4. Find the domain of the rational function.
f(x) =
a. {x|x ≠ -3, x ≠ 5}
b. {x|x ≠ 3, x ≠ -5}
c. all real numbers
d. {x|x ≠ 3, x ≠ -3, x ≠ -5}
Q5. Solve the equation in the real number system.
2. x3 + 9x2 + 26x + 24 = 0
a. {-4, -2, -3}
b. {2, 4}
c. {3, 2, 4}
d. {-4, -2}
Q6. Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1.
a. -3
b. -2
c. 3
d. 2
Q7. Use the Theorem for bounds on zeros to find a bound on the
real zeros of the polynomial function.
f(x) = x4 + 2x2 - 3
a. -4 and 4
b. -3 and 3
c. -6 and 6
d. -5 and 5
Q8. Find all zeros of the function and write the polynomial as a
product of linear factors.
f(x) = 3x4 + 4x3 + 13x2 + 16x + 4
a. f(x) = (3x - 1)(x - 1)(x + 2)(x - 2)
b. f(x) = (3x + 1)(x + 1)(x + 2i)(x - 2i)
c. f(x) = (3x - 1)(x - 1)(x + 2i)(x - 2i)
d. f(x) = (3x + 1)(x + 1)(x + 2)(x - 2)
Q9. Find the power function that the graph of f resembles for
large values of |x|.
f(x) = -x2(x + 4)3(x2 - 1)
a. y = x7
b. y = -x7
3. c. y = x3
d. y = x2
Q10. Use the Factor Theorem to determine whether x - c is a
factor of f(x).
8x3 + 36x2 - 19x - 5; x + 5
a. Yes
b. No
Q11. State whether the function is a polynomial function or not.
If it is, give its degree. If it is not, tell why not.
f(x) = 9x3 + 8x2 - 6
a. No; the last term has no variable
b. Yes; degree 5
c. Yes; degree 3
d. Yes; degree 6
Q12. Solve the equation in the real number system.
x4 - 3x3 + 5x2 - x - 10 = 0
a. {-1, -2}
b. {1, 2}
c. {-1, 2}
d. {-2, 1}
Q13. A developer wants to enclose a rectangular grassy lot that
borders a city street for parking. If the developer has 320 feet of
fencing and does not fence the side along the street, what is the
largest area that can be enclosed?
a. 25,600 ft2
b. 19,200 ft2
c. 12,800 ft2
d. 6400 ft2
4. Q14. State whether the function is a polynomial function or not.
If it is, give its degree. If it is not, tell why not.
f(x) =
a. Yes; degree 3
b. No; x is a negative term
c. No; it is a ratio
d. Yes; degree 1
Q15. Give the equation of the oblique asymptote, if any, of the
function.
h(x) =
a. y = 4x
b. y = 4
c. y = x + 4
d. no oblique asymptote
Q16. Find all of the real zeros of the polynomial function, then
use the real zeros to factor f over the real numbers.
f(x) = 3x4 - 6x3 + 4x2 - 2x + 1
a. no real roots; f(x) = (x2 + 1)(3x2 + 1)
b. 1, multiplicity 2; f(x) = (x - 1)2(3x2 + 1)
c. -1, 1; f(x) = (x - 1)(x + 1)(3x2 + 1)
d. -1, multiplicity 2; f(x) = (x + 1)2(3x2 + 1)
Q17. Determine whether the rational function has symmetry
with respect to the origin, symmetry with respect to the y-axis,
or neither.
f(x) =
a. symmetry with respect to the y-axis
b. symmetry with respect to the origin
c. neither
Q18. Find the vertex and axis of symmetry of the graph of the
function.
5. f(x) = -3x2 - 6x - 2
a. (-1, 1) ; x = -1
b. (2, -26) ; x = 2
c. (1, -11) ; x = 1
d. (-2, -8) ; x = -2
Q19. Find the indicated intercept(s) of the graph of the
function.
Q20. Determine, without graphing, whether the given quadratic
function has a maximum value or a minimum value and then
find that value.
f(x) = -x2 - 2x + 2
a. minimum; - 1
b. maximum; 3
c. minimum; 3
d. maximum; - 1
6. Q1. The logistic growth function f(t) =
describes the population of a species of butterflies tmonths after
they are introduced to a non-threatening habitat. How many
butterflies are expected in the habitat after 12 months?
a. 480 butterflies
b. 401 butterflies
c. 244 butterflies
d. 4800 butterflies
Q2. Find the present value. Round to the nearest cent.
To get $10,000 after 2 years at 18% compounded monthly
a. $5000.00
b. $6995.44
c. $8363.87
d. $11,956.18
7. Q3. A local bank advertises that it pays interest on savings
accounts at the rate of 3% compounded monthly. Find the
effective rate. Round answer to two decimal places.
a. 3.44%
b. 3.40%
c. 36%
d. 3.04%
Q4. The half-life of silicon-32 is 710 years. If 100 grams is
present now, how much will be present in 600 years? (Round
your answer to three decimal places.)
a. 0
b. 0.286
c. 94.311
d. 55.668
Q5. A fossilized leaf contains 12% of its normal amount of
carbon 14. How old is the fossil (to the nearest year)? Use 5600
years as the half-life of carbon 14.
a. 1031
b. 17,099
c. 20,040
d. 36,108
Q6. pH = -log10[H+] Find the [H+] if the pH = 8.4.
a. 3.98 x 10-8
b. 2.51 x 10-8
c. 3.98 x 10-9
d. 2.51 x 10-9
Q7. Express y as a function of x. The constant C is a positive
number.
ln y = ln 4x + ln C
8. a. y = 4Cx
b. y = 4x + C
c. y = (4x)C
d. y = x + 4C
Q8. Express as a single logarithm.
Q9. Find the amount that results from the investment.
$480 invested at 16% compounded quarterly after a period of 4
years
a. $864.45
b. $419.03
c. $869.11
d. $899.03
Q10. What principal invested at 8% compounded continuously
for 4 years will yield $1190? Round the answer to two decimal
places.
a. $864.12
b. $1188.62
c. $1638.78
d. $627.48
Q11. Change the exponential expression to an equivalent
expression involving a logarithm.
5x = 125
a. log125 x = 5
b. log5 125 = x
c. log125 5 = x
d. logx 125 = 5
Q12. Find functions f and g so that the composition of f and g is
H.
9. H(x) = |4 - 3x2|
a. f(x) = x2 ; g(x) = 4 - 3|x|
b. f(x) = 4 - 3|x|; g(x) = x2
c. f(x) = |x|; g(x) = 4 - 3x2
d. f(x) = 4 - 3x2 ; g(x) = |x|
Q13. The half-life of plutonium-234 is 9 hours. If 70 milligrams
is present now, how much will be present in 6 days? (Round
your answer to three decimal places.)
a. 0.689
b. 44.096
c. 0.001
d. 23.091
Q14. Solve the equation.
log327 = x
a. {81}
b. {9}
c. {3}
d. {30}
Q15. The function f(x) = 300(0.5) x/60 models the amount in
pounds of a particular radioactive material stored in a concrete
vault, where x is the number of years since the material was put
into the vault. Find the amount of radioactive material in the
vault after 170 years. Round to the nearest whole number.
a. 425 pounds
b. 42 pounds
c. 235 pounds
d. 53 pounds
10. Q16. Change the logarithmic expression to an equivalent
expression involving an exponent.
Q17. The function f is one-to-one. Find its inverse.
Q18. If the following defines a one-to-one function, find the
inverse.
{(6, 6), (12, 7), (10, 8), (8, 9)}
a. {(7, 6), (9, 10), (6, 10), (7, 8)}
b. {(7, 6), (6, 10), (6, 12), (7, 8)}
c. Not a one-to-one function
d. {(6, 6), (7, 12), (8, 10), (9, 8)}
Q19. Change the exponential expression to an equivalent
expression involving a logarithm.
ex = 25
a. log 25 x = e
b. log x e = 25
c. ln x = 25
d. ln 25 = x
Q20. Express as a single logarithm.
3log6x + 5log6(x - 6)
11. a. log6x3(x - 6)5
b. log6x(x - 6)15
c. log6x(x - 6)
d. 15 log6x(x - 6)
12.
13. Q1. Rob bought 2 pairs of shorts, 3 shirts and a pair of shoes for
$146.64. Jessie bought 3 pairs of shorts, 5 shirts and 2 pairs of
shoes for $256.35. Allen bought a pair of shorts and 4 shirts for
$104.07. What is the price of a pair of shorts? Express answer
rounded to two decimal places.
14. a. $14.55
b. $50.40
c. $22.38
d. $10.30
Q2. An 8-cylinder Crown Victoria gives 18 miles per gallon in
city driving and 21 miles per gallon in highway driving. A 300-
mile trip required 15.5 gallons of gasoline. How many whole
miles were driven in the city?
a. 153 miles
b. 168 miles
c. 147 miles
d. 132 miles
Q3. A retired couple has $190,000 to invest to obtain annual
income. They want some of it invested in safe Certificates of
Deposit yielding 7%. The rest they want to invest in AA bonds
yielding 10% per year. How much should they invest in each to
realize exactly $17,200 per year?
a. $120,000 at 7% and $70,000 at 10%
b. $130,000 at 7% and $60,000 at 10%
c. $130,000 at 10% and $60,000 at 7%
d. $140,000 at 10% and $50,000 at 7%
Q4. Verify that the values of the variables listed are solutions of
the system of equations.
x = 5, y = 5
a. not a solution
b. solution
Q5. Use Cramer's rule to solve the linear system.
a. x = 2, y = 4
b. x = 4, y = 2
15. c. x = -2, y = 4
d. x = -4, y = -2
Q6. A flat rectangular piece of aluminum has a perimeter of 62
inches. The length is 15 inches longer than the width. Find the
width.
a. 31 inches
b. 38 inches
c. 8 inches
d. 23 inches
Q7. Verify that the values of the variables listed are solutions of
the system of equations.
x = 0, y = -5, z =-4
a. solution
b. not a solution
Q8. Write the partial fraction decomposition of the rational
expression.
Q9. Solve the system using the inverse method.
a. x = -36, y = -38, z = -14
b. x = -14, y = 88, z = -32
c. x = -60, y = 82, z = -34
d. x = 8, y = 24, z = 10
Q10. Solve the system using the inverse method.
a. x = -19, y = -61, z = -35
b. x = -1, y = -3, z = -2
c. x = 15, y = -49, z = 27
16. d. x = -2, y = -28, z = 20
Q11. Perform the indicated operations and simplify.
Q12. Write the partial fraction decomposition of the rational
expression.
Q13. Solve the system.
a. inconsistent (no solution)
b. (-9, 0)
c. (0, 0)
d. y = - x/2 - 9, where x is any real number
Q14. Find the inverse of the matrix.
A=
Q15. A movie theater charges $8.00 for adults and $5.00 for
children. If there were 40 people altogether and the theater
collected $272.00 at the end of the day, how many of them were
adults?
a. 16 adults
b. 10 adults
c. 29 adults
d. 24 adults
Q16. The Family Fine Arts Center charges $21 per adult and
$12 per senior citizen for its performances. On a recent
weekend evening when 486 people paid admission, the total
receipts were $6894. How many who paid were senior citizens?
a. 208 senior citizens
17. b. 368 senior citizens
c. 118 senior citizens
d. 278 senior citizens
Q17. Use the elimination method to solve the system.
a. x = 11, y = -11
b. x = -2, y = 9
c. x = 9, y = -9
d. x = -9, y = 9
Q18. Use the properties of determinants to find the value of the
second determinant, given the value of the first.
&
a. -44
b. 44
c. 88
d. -88
Q19. Jenny receives $1270 per year from three different
investments totaling $20,000. One of the investments pays 6% ,
the second one pays 8%, and the third one pays 5%. If the
money invested at 8% is $1500 less than the amount invested at
5%, how much money has Jenny invested in the investment that
pays 6%?
a. $8500
b. $4500
c. $10,000
d. $1500
Q20. Solve the system of equations.
18. a. x = 0, y = 1, z = 0
b. x = 1, y =1, z = 1
c. x = 0, y = 1, z = -1
d. x = 0, y = 0, z = 1