Math Quiz
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College Algebra MATH 107 Spring, 2020
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MATH 107 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 30 problems.
Problems #1–12 are Multiple Choice.
Problems #13–21 are Short Answer. (Work not required to be shown)
Problems #22–30 are Short Answer with work required to be shown.
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function. 1. ______
A. Domain [– 4, 2]; Range [– 2, 4]
B. Domain [– 2, 4]; Range [– 2, 1]
C. Domain [– 2, 4]; Range [– 4 , 2]
D. Domain [0, 2]; Range [– 2, 0]
2. Solve: 3 10x x+ = − 2. ______
A. No solution
B. –2, 5
C. 5
D. –2
-2 2 4 -4
-2
-4
2
4
College Algebra MATH 107 Spring, 2020
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3. Determine the interval(s) on which the function is decreasing. 3. ______
A. (–1, 3)
B. (–2, 4)
C. (–3.6, 0) and (6.7, )
D. (–, –2) and (4, )
4. Determine whether the graph of 2y x= + is symmetric with respect to the origin,
the x-axis, or the y-axis. 4. ______
A. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and
not symmetric with respect to the origin
B. symmetric with respect to the x-axis only
C. symmetric with respect to the y-axis only
D. symmetric with respect to the origin only
5. Solve, and express the answer in interval notation: | 5 – 6x | 13. 5. ______
A. (–, 3] [−4/3, )
B. (–, −4/3] [3, )
C. [4/3, )
D. [–4/3, 3]
College Algebra MATH 107 Spring, 2020
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6. Which of the following represents the graph of 8x − 3y = 24 ? 6. ______
A. B.
C. D.
College Algebra MATH 107 Spring, 2020
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7. Write a slope-intercept equation for a line parallel to the line x + 7y = 9 which passes through
the point (28, –3). 7. ______
A. 25y x=− +
B. 1
1 7
y x= − +
C. 1
3 7
y x= − −
D. 1
7 7
y x= −
8. Which of the following best describes the graph? 8. ______
A. It is the graph of a function but not one-to-one.
B. It is the graph of a function and it is one-to-one.
C. It is not the graph of a function.
D. It is the graph of an absolute value relation.
.
College Algebra MATH 107 Spring, 2020
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9. Write as an equivalent expression: log (x – 3) – 8 log y + log 1 9. ______
A. log( 3)
log(8 )
x
y
−
B. 2
log 8
x
y
−
C. 8
3 log
x
y
−
D. ( )log 2 8x y− −
10. Which of the functions corresponds to the graph? 10. ______
A. ( ) 2 xf x e−=
B. ( ) 2 xf x e−= +
C. ( ) 2 xf x e= −
D. ( ) 2xf x e−=
College Algebra MATH 107 Spring, 2020
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11. Suppose that for a function f, the equation f (x) = 0 has no real-number solution.
Which of the following statements MUST be true? 11. ______
A. f is an invertible function.
B. The graph of f is a horizontal line.
C. f has no x-intercept.
D. f has no y-intercept.
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)?
12. ______
y = f (x) y = g(x)
A. g(x) = f (x) – 4
B. g(x) = f (x) + 4
C. g(x) = f (x + 4)
D. g(x) = f (x – 4)
2 4 -2-4
-2
-4
2
4
2 4 -2-4
-2
-4
2
4
College Algebra MATH 107 Spring, 2020
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SHORT ANSWER:
13. Multiply and simplify: (8 − i)(5 + 7i).
Write the answer in the form a + bi, where a and b are real numbers. Answer: ________
14. Solve, and write the answer in interval notation: 7
0 9
x
x
−
− . Answer: ________
15. A bowl of soup at 175 F. is placed in a room of constant temperature of 70 F. The
temperature T of the soup t minutes after it is placed in the room is given by
T(t) = 70 + 105 e – 0.075 t
Find the temperature of the soup 18 minutes after it is placed in the room. (Round to the nearest degree.)
Answer: ________
16. Find the value of the logarithm: 4 1
log 64
. Answer: ________
17. Solve: 4 97 49x+ = . Answer: ________
18. Suppose $4,700 is invested in an account at an annual interest rate of 5.2% compounded
continuously. How long (to the nearest tenth of a year) will it take the investment to double in
size? Answer: ________
19. Let f (x) = x2 − 10x + 23.
(a) Find the vertex. Answer: ________
(b) State the range of the function. Answer: ________
(c) On what interval is the function decreasing? Answer: ________
College Algebra MATH 107 Spring, 2020
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20. Consider the polynomial P(x), shown in both standard form and factored form.
3 21 7 7 1 ( ) 5 ( 1)( 3)( 5)
3 3 3 3 P x x x x x x x= − + − − = − + − −
(a) Which sketch illustrates the end behavior of the polynomial function?
Answer: ________
(b) State the zeros of the function. Answer: ________________
(c) State the y-intercept. Answer: ________________
(d) State which graph below is the graph of P(x). Answer: ________
GRAPH A GRAPH B
GRAPH C GRAPH D
A. B. C. D.
vvvv
vvvv vvvv vvvv
College Algebra MATH 107 Spring, 2020
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21. Let 4
)( 2 −
= x
x xf .
(a) State the domain. Answer: _________________
(b) State the horizontal asymptote. Answer: _________________
(c) State the vertical asymptote(s). Answer: _________________
(d) Which of the following represents the graph of 4
)( 2 −
= x
x xf ? Answer: ______________
GRAPH A. GRAPH B.
GRAPH C. GRAPH D.
College Algebra MATH 107 Spring, 2020
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SHORT ANSWER, with work required to be shown, as indicated.
22. Let xxf −= 9)( and g(x) = x + 1.
(a) Find )7(−
g
f . Show work.
(b) Find the domain of the quotient function g
f . Explain.
23. Points (–3, 2) and (1, 6) are endpoints of the diameter of a circle.
(a) What is the length of the diameter? Give the exact answer, 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 (–7, 4) and (–9, 8). Write the
equation in slope-intercept form. Show work.
25. A salesperson earns a base salary of $1,650 per month and a commission of 5.3% on the
amount of sales made. If the salesperson has a paycheck of $3425.50 for one month, what was
the amount of sales for the month? Show work.
26. Let f (x) = 5x2 – 3 and g(x) = x – 4.
(a) Find the composite function ))(( xgf and simplify. Show work.
(b) Find ( ) ( 1)f g −o . Show work.
27. Find the exact solutions and simplify as much as possible: 9x2 + 10 = 20x. Show work.
28. Given the function 1
( ) 3 7
f x x= − , find a formula for the inverse function. Show work.
College Algebra MATH 107 Spring, 2020
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29. The Travel Time bus company has determined that when x tourists are given a particular bus
tour, the profit P (in dollars) is given by
P(x) = –0.25 x2 + 25.50x – 220
(a) What is the company’s profit if 32 tourists are given the tour?
(b) How many tourists should be given the tour in order to maximize the company’s profit?
Show work.
30. Solve: 2
7 12 0
6 36
x
x x
+ + =
+ − . Show work.
