College Algebra MATH 107 Spring, 2019, V4.2
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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 [–1, 3]; Range [–2, 2]
B. Domain [–1, 3]; Range [–1, 1]
C. Domain [–2, –1]; Range [1, 2]
D. Domain [–2, 2]; Range [–1, 3]
2. Solve: 35 7x x+ = − 2. ______
A. No solution
B. 1
C. 14
D. 1, 14
2 4 -4
-2
-4
2
4
-2
College Algebra MATH 107 Spring, 2019, V4.2
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3. Determine the interval(s) on which the function is decreasing. 3. ______
A. ( ),0− and ( )2,
B. ( ), 5 / 3− − , ( )0,2 , and ( )11/ 3,
C. ( )1,1− and ( )3,
D. ( ), 4 / 3−
4. Determine whether the graph of 8y x += is symmetric with respect to the origin,
the x-axis, or the y-axis. 4. ______
A. symmetric with respect to the y-axis only
B. symmetric with respect to the x-axis only
C. symmetric with respect to the origin only
D. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and
not symmetric with respect to the origin
5. Solve, and express the answer in interval notation: | 8 – 3x | 4. 5. ______
A. [4/3, )
B. [4/3, 4]
C. (–, 4] [4/3, )
D. (–, 4/3] [4, )
College Algebra MATH 107 Spring, 2019, V4.2
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6. Which of the following represents the graph of 7x − 4y = 28 ? 6. ______
A. B.
C. D.
College Algebra MATH 107 Spring, 2019, V4.2
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7. Write a slope-intercept equation for a line parallel to the line x + 3y = 8 which passes through
the point (– 4, 5). 7. ______
A. 1
5 3
y x= +
B. 1 11
3 3 y x= − +
C. 1
5 3
y x= − +
D. 3 7y x= − −
8. Does the graph below represent a function and is it one-to-one? 8. ______
A. It is a function and it is one-to-one.
B. It is a function but not one-to-one.
C. It is not a function but it is one-to-one.
D. It is not a function and it is not one-to-one.
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9. Express as an equivalent expression: log (x + 4) – 2 log y + log 1 9. ______
A. ( )log 5 2x y+ −
B. 2
log( 4)
log( )
x
y
+
C. 5
log 2
x
y
+
D. 2
4 log
x
y
+
10. Which of the functions corresponds to the graph? 10. ______
A. ( ) 1xf x e−= −
B. ( ) 1xf x e−= +
C. ( ) 2xf x e= −
D. ( ) xf x e= −
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11. Suppose that for a function f , the equation f (x) = 0 has no real-number solutions.
Which of the following statements MUST be true? 11. ______
A. f (x) > 0 for all x in the domain of f.
B. f is an invertible function.
C. f has no x-intercepts.
D. f has no y-intercepts.
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 – 1) – 1
B. g(x) = f (x – 1) + 1
C. g(x) = f (x + 1) – 1
D. g(x) = f (x + 1) + 1
2 4 -2 -4
-2
-4
2
4
2 4 -2 -4
-2
-4
2
4
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SHORT ANSWER:
13. Multiply and simplify: (6 − 7i)(8 + 5i).
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: 2
0 9
x
x
+
− . Answer: ________
15. A bowl of soup at 190 F. is placed in a room of constant temperature of 80 F. The
temperature T of the soup t minutes after it is placed in the room is given by
T(t) = 80 + 110 e – 0.075 t
Find the temperature of the soup 8 minutes after it is placed in the room. (Round to the nearest degree.) Answer: ________
16. Find the value of the logarithm: 6 1
log 36
. Answer: ________
17. Solve: 5 34 16x+ = . Answer: ________
18. Suppose $6,600 is invested in an account at an annual interest rate of 3.7% 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 + 27.
(a) Find the vertex. Answer: ________
(b) State the range of the function. Answer: ________
(c) On what interval is the function decreasing? Answer: ________
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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?
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
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21. Let 3 2
( ) 2
x f x
x
− =
− .
(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 3 2
( ) 2
x f x
x
− =
− ? Answer: ______________
GRAPH A. GRAPH B.
GRAPH C. GRAPH D.
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SHORT ANSWER, with work required to be shown, as indicated.
22. Let f (x) = x − 12 and 8)( −= xxg .
(a) Find )9(
g
f . Show work.
(b) Find the domain of the quotient function g
f . Explain.
23. Points (–6, 1) and (4, 3) 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 (6, –2) and (1, 8). Write the
equation in slope-intercept form. Show work.
25. Maria, a resident of Metropolis, pays Metropolis an annual tax of $60 plus 2.2% of her
annual income. If Maria paid $1,237 in tax, what was Maria’s income? Show work.
26. Let f (x) = 3×2 + 7 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: 2×2 = 3 + 8x. Show work.
28. Given the function 1
( ) 4 8
f x x= − , find a formula for the inverse function. Show work.
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29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P, in
dollars is given by
P(x) = –0.001 x2 + 1.3x – 45
(a) What is the company’s profit if 900 donuts are made daily?
(b) How many donuts should be made daily in order to maximize the company’s profit? Show
work.
30. Solve: 2
0 7 24
3 9
x
x x =
− +
− − . Show work.
