1. Write an equation in standard form of the parabola that has th.docx

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)
D. x = 1, x = 2, x = -4; f(x) crosses the x-axis at 2 and -4; f(x)
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 coordinates of the vertex for the parabola defined by
the given quadratic function.
f(x) = -2(x + 1)
2
+ 5
A. (-1, 5)
B. (2, 10)
C. (1, 10)
D. (-3, 7)
14 of 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) = -2x
4
+ 4x
3
A. x = 1, x = 0; f(x) touches the x-axis at 1 and 0
B. x = -1, x = 3; f(x) crosses the x-axis at -1 and 3
C. x = 0, x = 2; f(x) crosses the x-axis at 0 and 2
D. x = 4, x = -3; f(x) crosses the x-axis at 4 and -3

15 of 20
Find the domain of the following rational function.
f(x) = 5x/x - 4
A. {x │x ≠ 3}
B. {x │x = 5}
C. {x │x = 2}
D. {x │x ≠ 4}
16 of 20
Based on the synthetic division shown, the equation of the slant
asymptote of f(x) = (3x
2
- 7x + 5)/x – 4 is:
A. y = 3x + 5.
B. y = 6x + 7.
C. y = 2x - 5.
D. y = 3x
2
+ 7.
17 of 20
The perimeter of a rectangle is 80 feet. If the length of the
rectangle is represented by x, its width can be expressed as:
A. 80 + x.
B. 20 - x.
C. 40 + 4x.

D. 40 - x.
18 of 20
Use the Intermediate Value Theorem to show that each
polynomial has a real zero between the given integers.
f(x) = 2x
4
- 4x
2
+ 1; between -1 and 0
A. f(-1) = -0; f(0) = 2
B. f(-1) = -1; f(0) = 1
C. f(-1) = -2; f(0) = 0
D. f(-1) = -5; f(0) = -3
19 of 20
Solve the following polynomial inequality.
9x
2
- 6x + 1 < 0
A. (-∞, -3)
B. (-1, ∞)
C. [2, 4)
D. Ø
20 of 20
Use the Intermediate Value Theorem to show that each
polynomial has a real zero between the given integers.
f(x) = x

3
- x - 1; between 1 and 2
A. f(1) = -1; f(2) = 5
B. f(1) = -3; f(2) = 7
C. f(1) = -1; f(2) = 3
D. f(1) = 2; f(2) = 7
1. Find the domain of following logarithmic function.
f(x) = ln (x - 2)
2
A. (∞, 2) ∪ (-2, -∞)
B. (-∞, 2) ∪ (2, ∞)
C. (-∞, 1) ∪ (3, ∞)
D. (2, -∞) ∪ (2, ∞)
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I
2 .
Solve the following exponential equation. Express the solution
set in terms of natural logarithms or common logarithms to a
decimal approximation, of two decimal places, for the solution.
e
x
= 5.7
A. {ln 5.7}; ≈1.74
B. {ln 8.7}; ≈3.74

C. {ln 6.9}; ≈2.49
D. {ln 8.9}; ≈3.97
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3.
Evaluate the following expression without using a calculator.
Log
7
√7
A. 1/4
B. 3/5
C. 1/2
D. 2/7
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4.
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
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5.
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
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6.
The half-life of the radioactive element krypton-91 is 10
seconds. If 16 grams of krypton-91 are initially present, how
many grams are present after 10 seconds? 20 seconds?
A. 10 grams after 10 seconds; 6 grams after 20 seconds
B. 12 grams after 10 seconds; 7 grams after 20 seconds
C. 4 grams after 10 seconds; 1 gram after 20 seconds
D. 8 grams after 10 seconds; 4 grams after 20 seconds
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7.
Use properties of logarithms to expand the following
logarithmic expression as much as possible.
log
b
(x
2
y)
A. 2 log
y
x + log
x
y
B. 2 log
b
x + log
b
y

C. log
x
- log
b
y
D. log
b
x – log
x
y
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8.
Solve the following exponential equation by expressing each
side as a power of the same base and then equating exponents.
e
x+1
= 1/e
A. {-3}
B. {-2}
C. {4}
D. {12}
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9.
Use properties of logarithms to condense the following
logarithmic expression. Write the expression as a single
logarithm whose coefficient is 1.

log x + 3 log y
A. log (xy)
B. log (xy
3
)
C. log (xy
2
)
D. log
y
(xy)
3
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10.
Approximate the following using a calculator; round your
answer to three decimal places.
e
-0.95
A. .483
B. 1.287
C. .597
D. .387
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11.

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
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12.
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}
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13.
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}
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14.
Find the domain of following logarithmic function.
f(x) = log (2 - x)
A. (∞, 4)
B. (∞, -12)
C. (-∞, 2)
D. (-∞, -3)
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15.
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
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16.
Solve the following exponential equation. Express the solution
set in terms of natural logarithms or common logarithms to a
decimal approximation, of two decimal places, for the solution.
3
2x
+ 3
x
- 2 = 0
A. {1}
B. {-2}
C. {5}
D. {0}
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17.
You have $10,000 to invest. One bank pays 5% interest
compounded quarterly and a second bank pays 4.5% interest
compounded monthly. Use the formula for compound interest to
write a function for the balance in each bank at any time t.

A. A = 20,000(1 + (0.06/4))
4t
; A = 10,000(1 + (0.044/14))
12t
B. A = 15,000(1 + (0.07/4))
4t
; A = 10,000(1 + (0.025/12))
12t
C. A = 10,000(1 + (0.05/4))
4t
; A = 10,000(1 + (0.045/12))
12t
D. A = 25,000(1 + (0.05/4))
4t
; A = 10,000(1 + (0.032/14))
12t
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18.
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, ∞)

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19.
log
6
216 = y
A. 6
y
= 216
B. 6
x
= 216
C. 6
logy
= 224
D. 6
xy
= 232
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20.
5 = log
b
32
A. b

5
= 32
B. y
5
= 32
C. B
log5
= 32
D. Log
b
= 32
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21.
Perform the long division and write the partial fraction
decomposition of the remainder term.
x
5
+ 2/x
2
- 1
A. x
2
+ x - 1/2(x + 1) + 4/2(x - 1)
B. x
3
+ x - 1/2(x + 1) + 3/2(x - 1)
C. x
3

+ x - 1/6(x - 2) + 3/2(x + 1)
D. x
2
+ x - 1/2(x + 1) + 4/2(x - 1)
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22.
Solve each equation by the substitution method.
x + y = 1
x
2
+ xy – y
2
= -5
A. {(4, -3), (-1, 2)}
B. {(2, -3), (-1, 6)}
C. {(-4, -3), (-1, 3)}
D. {(2, -3), (-1, -2)}
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23.
A television manufacturer makes rear-projection and plasma
televisions. The proﬁt per unit is $125 for the rear-projection
televisions and $200 for the plasma televisions.
Let x = the number of rear-projection televisions manufactured
in a month and let y = the number of plasma televisions
manufactured in a month. Write the objective function that
models the total monthly profit.

A. z = 200x + 125y
B. z = 125x + 200y
C. z = 130x + 225y
D. z = -125x + 200y
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24. Solve the following system by the substitution method.
{x + 3y = 8
{y = 2x - 9
A. {(5, 1)}
B. {(4, 3)}
C. {(7, 2)}
D. {(4, 3)}
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25.
Solve the following system by the addition method.
{4x + 3y = 15
{2x – 5y = 1
A. {(4, 0)}
B. {(2, 1)}
C. {(6, 1)}

D. {(3, 1)}
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26.
Many elevators have a capacity of 2000 pounds.
If a child averages 50 pounds and an adult 150 pounds, write an
inequality that describes when x children and y adults will
cause the elevator to be overloaded.
A. 50x + 150y > 2000
B. 100x + 150y > 1000
C. 70x + 250y > 2000
D. 55x + 150y > 3000
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27.
Find the quadratic function y = ax
2
+ bx + c whose graph passes through the given points.
(-1, -4), (1, -2), (2, 5)
A. y = 2x
2
+ x - 6
B. y = 2x
2
+ 2x - 4
C. y = 2x
2

+ 2x + 3
D. y = 2x
2
+ x - 5
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28.
Write the partial fraction decomposition for the following
rational expression.
x + 4/x
2
(x + 4)
A. 1/3x + 1/x
2
- x + 5/4(x
2
+ 4)
B. 1/5x + 1/x
2
- x + 4/4(x
2
+ 6)
C. 1/4x + 1/x
2
- x + 4/4(x
2
+ 4)
D. 1/3x + 1/x
2

- x + 3/4(x
2
+ 5)
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29.
Find the quadratic function y = ax
2
+ bx + c whose graph passes through the given points.
(-1, 6), (1, 4), (2, 9)
A. y = 2x
2
- x + 3
B. y = 2x
2
+ x
2
+ 9
C. y = 3x
2
- x - 4
D. y = 2x
2
+ 2x + 4
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30.
Solve the following system.
3(2x+y) + 5z = -1

2(x - 3y + 4z) = -9
4(1 + x) = -3(z - 3y)
A. {(1, 1/3, 0)}
B. {(1/4, 1/3, -2)}
C. {(1/3, 1/5, -1)}
D. {(1/2, 1/3, -1)}
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31.
On your next vacation, you will divide lodging between large
resorts and small inns. Let x represent the number of nights
spent in large resorts. Let y represent the number of nights
spent in small inns.
Write a system of inequalities that models the following
conditions:
You want to stay at least 5 nights. At least one night should be
spent at a large resort. Large resorts average $200 per night and
small inns average $100 per night. Your budget permits no more
than $700 for lodging.
A.
y ≥ 1
x + y ≥ 5
x ≥ 1
300x + 200y ≤ 700
B.
y ≥ 0
x + y ≥ 3
x ≥ 0
200x + 200y ≤ 700

C.
y ≥ 1
x + y ≥ 4
x ≥ 2
500x + 100y ≤ 700
D.
y ≥ 0
x + y ≥ 5
x ≥ 1
200x + 100y ≤ 700
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32.
2x + 4y + 3z = 2
x + 2y - z = 0
4x + y - z = 6
A. {(-3, 2, 6)}
B. {(4, 8, -3)}
C. {(3, 1, 5)}
D. {(1, 4, -1)}
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33.
x = y + 4
3x + 7y = -18
A. {(2, -1)}

B. {(1, 4)}
C. {(2, -5)}
D. {(1, -3)}
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34.
4/2x
2
- 5x – 3
A. 4/6(x - 2) - 8/7(4x + 1)
B. 4/7(x - 3) - 8/7(2x + 1)
C. 4/7(x - 2) - 8/7(3x + 1)
D. 4/6(x - 2) - 8/7(3x + 1)
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35.
Solve each equation by either substitution or addition method.
x
2
+ 4y
2
= 20
x + 2y = 6
A. {(5, 2), (-4, 1)}

B. {(4, 2), (3, 1)}
C. {(2, 2), (4, 1)}
D. {(6, 2), (7, 1)}
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36. Solve each equation by either substitution or addition
method.
x
2
+ 4y
2
= 20
x + 2y = 6
A. {(5, 2), (-4, 1)}
B. {(4, 2), (3, 1)}
C. {(2, 2), (4, 1)}
D. {(6, 2), (7, 1)}
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37.
1/x
2
– c
2

(c ≠ 0)
A. 1/4c/x - c - 1/2c/x + c
B. 1/2c/x - c - 1/2c/x + c
C. 1/3c/x - c - 1/2c/x + c
D. 1/2c/x - c - 1/3c/x + c
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38.
x
2
- 4y
2
= -7
3x
2
+ y
2
= 31
A. {(2, 2), (3, -2), (-1, 2), (-4, -2)}
B. {(7, 2), (3, -2), (-4, 2), (-3, -1)}
C. {(4, 2), (3, -2), (-5, 2), (-2, -2)}
D. {(3, 2), (3, -2), (-3, 2), (-3, -2)}
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39.

y
2
= x
2
- 9
2y = x – 3
A. {(-6, -4), (2, 0)}
B. {(-4, -4), (1, 0)}
C. {(-3, -4), (2, 0)}
D. {(-5, -4), (3, 0)}
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40.
ax +b/(x – c)
2
(c ≠ 0)
A. a/a – c +ac + b/(x – c)
2
B. a/b – c +ac + b/(x – c)
C. a/a – b +ac + c/(x – c)
2
D. a/a – b +ac + b/(x – c)
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