The document contains a 30-question math exam covering topics like functions, graphs, equations, inequalities, logarithms, and other math concepts. It includes multiple choice, short answer, and show work questions assessing skills like domain and range, solving equations, graphing, composites, inverses, lines, maximizing profit, and more. Students must demonstrate mathematical reasoning and problem-solving abilities.

1. 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

2. 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

3. 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).

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.

5. 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.

6. 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) – 3
SHORT ANSWER:
13. Multiply and simplify: (7 − 4i)2.
Write the answer in the form a + bi, where a and b are real
numbers.
14. Solve, and write the answer in interval notation:
15. Water initially at 200° F. is left in a room of temperature
70° F to cool.

7. After t minutes, the temperature T of the water is given by T(t)
= 70 + 130e–0.096t
Find the temperature of the water 10 minutes after it is left to
cool. (Round to the nearest degree.)
16. Find the value of the logarithm:
17. Solve: 35x-4 =
9.
18. Suppose $1,900 is invested in an account at an annual
interest rate of 6.6% compounded continuously. How long (to
the nearest tenth of a year) will it take the investment to double
in
size?
19. Let f(x) = x2 + 20x + 97.
(a) Find the
vertex.
(b) State the range of the

8. function.
(c) On what interval is the function
decreasing?
20. Consider the polynomial P(x), shown in both standard form
and factored form.
(a) Which sketch illustrates the end behavior of the polynomial
function?
(b) State the zeros of the
function.
(c) State the y-
intercept.
(d) State which graph below is the graph of
P(x).

9. 21. Let
(a) State the
domain.
(b) State the horizontal
asymptote.
(c) State the vertical
asymptote(s).
(d) Which of the following represents the graph of ?
SHORT ANSWER, with work required to be shown, as
indicated.
22. Let and .
(a) Find . Show work.
(b) Find the domain of the quotient function . Explain.
23. Points (3, –1) and (7, –9) are endpoints of the diameter of a
circle.
(a) What is the length of the diameter? Give the exact answer,

10. simplified as much as possible. Show work.
(b) What is the center point C of the circle?
(c) Given the point C you found in part (b), state the point
symmetric to C about the x-axis.
24. Find the equation for a line which passes through the points
(– 3, 2) and (– 6, 8). Write the equation in slope-intercept
form. Show work.
25. A salesperson earns a base salary of $1,475 per month and a
commission of 8.4% on the amount of sales. If the salesperson
has a paycheck of $4,637.60 for one month, what was the
amount of sales for the month? Show work
26. Let f(x) = 8x2 – 10 and g(x) = x – 2.
(a) Find the composite function and simplify. Show work.
(b) Find . Show work.
27. Find the exact solutions and simplify as much as possible:
2x2 − 1 = 6x. Show work.

11. 2x2 – 6x – 1 = 0
28. Given the function, find a formula for the inverse
function. Show work.
29. Donut Delights, Inc. has determined that when x donuts are
made daily, the profit P (in dollars) is given by
(a) What is the company’s profit if 500 donuts are made daily?
(b) How many donuts should be made daily in order to
maximize the company’s profit? Show work.
30. Solve: . Show work.
However, the solution x = -4 must be discarded as it
will make the denominators of the original equation
equal to 0.

12. Solution
: x = -3