College Algebra MATH 107 Spring, 2016, V4.7 Page 1 of 11 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 [–3, 1] B. Domain [–1, 1]; Range [–1, 3] C. Domain [–1/2, 0]; Range [–1, 0] D. Domain [–3, 1]; Range [–1, 3] 2. Solve: 17 3x x+ = − 2. ______ A. No solution B. −1 C. −7 D. −1, 8 2 4 -4 -2 -4 2 4 -2 College Algebra MATH 107 Spring, 2016, V4.7 Page 2 of 11 3. Determine the interval(s) on which the function is increasing. 3. ______ A. (–2, 4) B. (–∞, –2) and (4, ∞) C. (–3.6, 0) and (6.7, ∞) D. (–3, 1) 4. Determine whether the graph of 7y 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: | 6 – 5x | ≤ 14. 5. ______ A. [–8/5, 4] B. (–∞, −8/5] ∪ [4, ∞) C. (–∞, –8/5] D. [4, ∞) College Algebra MATH 107 Spring, 2016, V4.7 Page 3 of 11 6. Which of the following represents the graph of 8x + 3y = 24 ? 6. ______ A. B. C. D. College Algebra MATH 107 Spring, 2016, V4.7 Page 4 of 11 7. Write a slope-intercept equation for a line parallel to the line x – 7y = 2 which passes through the point (14, –9). 7. ______ A. 1 7 7 y x= − − B. 7 89y x= − + C. 1 9 7 y x= − D. 1 11 7 y x= − 8. Which of the following best describes the graph? 8. ______ 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. College Algebra MATH 107 Spring, 2016, V4.7 Page 5 of 11 9. Express as a single logarithm: 5 log y – log (x + 1) + log 1 9. ______ A. log(5 ) log( 1) y x + B. ( )log 5 y x− C. 5 log 1 y x     +  D. 5 ...

1. College Algebra MATH 107 Spring, 2016, V4.7
Page 1 of 11
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. ______

2. A. Domain [–1, 3]; Range [–3, 1]
B. Domain [–1, 1]; Range [–1, 3]
C. Domain [–1/2, 0]; Range [–1, 0]
D. Domain [–3, 1]; Range [–1, 3]
2. Solve: 17 3x x+ = − 2. ______
A. No solution
B. −1
C. −7
D. −1, 8
2 4 -4
-2
-4

3. 2
4
-2
College Algebra MATH 107 Spring, 2016, V4.7
Page 2 of 11
3. Determine the interval(s) on which the function is increasing.
3. ______
A. (–2, 4)
B. (–∞, –2) and (4, ∞)
C. (–3.6, 0) and (6.7, ∞)
D. (–3, 1)

4. 4. Determine whether the graph of 7y 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: | 6 – 5x |
≤ 14. 5. ______
A. [–8/5, 4]
B. (–∞, −8/5] ∪ [4, ∞)
C. (–∞, –8/5]
D. [4, ∞)
College Algebra MATH 107 Spring, 2016, V4.7

5. Page 3 of 11
6. Which of the following represents the graph of 8x + 3y = 24
? 6. ______
A. B.
C. D.
College Algebra MATH 107 Spring, 2016, V4.7
Page 4 of 11
7. Write a slope-intercept equation for a line parallel to the line
x – 7y = 2 which passes through
the point (14, –9). 7. ______
A.
1
7
7

6. y x= − −
B. 7 89y x= − +
C.
1
9
7
y x= −
D.
1
11
7
y x= −
8. Which of the following best describes the graph? 8. ______
A. It is the graph of a function and it is one-to-one.

7. 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.
College Algebra MATH 107 Spring, 2016, V4.7
Page 5 of 11
9. Express as a single logarithm: 5 log y – log (x + 1) + log 1
9. ______
A.
log(5 )
log( 1)
y
x +
B. ( )log 5 y x−
C.
5
log
1

8. y
x
D.
5 1
log
1
y
x
10. Which of the functions corresponds to the graph? 10.
______
A. ( ) 2 xf x e=

9. B. ( ) 1 xf x e= +
C. ( ) 2 xf x e= +
D. ( ) 2 xf x e=
College Algebra MATH 107 Spring, 2016, V4.7
Page 6 of 11
11. Suppose that for a function f , the equation f (x) = 0 has
exactly three real-number solutions.
Which of the following statements MUST be true?
11. ______
A. f is a cubic polynomial function.
B. f has exactly three x-intercepts.
C. f has exactly three y-intercepts.
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

10. 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 + 2) – 1
B. g(x) = f (x – 2) + 2
C. g(x) = f (x – 1) – 2
D. g(x) = f (x + 1) – 2
2 4 -2 -4
-2
-4
2

11. 4
y = f(x)
2 4 -2 -4
-2
-4
2
4
College Algebra MATH 107 Spring, 2016, V4.7
Page 7 of 11
SHORT ANSWER:
13. Multiply and simplify: (6 + 5i)(9 + i).
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:
9
0
3
x

12. x
+
≤
−
. Answer: ________
15. A bowl of soup at 165° F. is placed in a room of constant
temperature of 75° F. The
temperature T of the soup t minutes after it is placed in the
room is given by
T(t) = 75 + 90 e
– 0.075 t
Find the temperature of the soup 20 minutes after it is placed in
the room. (Round to the nearest
degree.)
Answer: ________
16. Find the value of the logarithm: 4
1
log
16

13. . Answer: ________
17. Solve:
5 87 49x + = . Answer: ________
18. Suppose $4,400 is invested in an account at an annual
interest rate of 3.4% 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) = x
2
−−−− 2x −−−− 5.
(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, 2016, V4.7

14. Page 8 of 11
20. Consider the polynomial P(x), shown in both standard form
and factored form.
4 3 21 1 7 41 1
( ) 3 ( 3)( 1)( 2)( 5)
10 2 10 10 10
P x x x x x x x x x= + − − − = − + + +
(a) Which sketch illustrates the end behavior of the polynomial
function?
Answer: ________
(b) State the y-intercept. Answer: ________________
(c) State the zeros of the function. Answer: ________________
(d) State which graph below is the graph of P(x). Answer:
________
GRAPH A GRAPH B
GRAPH C GRAPH D

15. A.
B. C. D.
vvvv
vvvv
vvvv vvvv
College Algebra MATH 107 Spring, 2016, V4.7
Page 9 of 11
21. Let
4
)(
2
−
=
x
x
xf .
(a) State the domain. Answer: _________________

16. (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, 2016, V4.7

17. Page 10 of 11
SHORT ANSWER, with work required to be shown, as
indicated.
22. Let f (x) = x + 2 and xxg −= 6)( .
g
f
. Show work.
(b) Find the domain of the quotient function
g
f
. Explain.
23. Points (7, – 6) and (9, 2) are endpoints of the diameter of a
circle.
(a) What is the length of the diameter? Give the exact answer,

18. 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 y-axis.
24. Find the equation for a line which passes through the points
(6, 8) and (2, – 4). Write the
equation in slope-intercept form. Show work.
25. A salesperson earns a base salary of $2,100 per month and a
commission of 5.8% on the
amount of sales made. If the salesperson has a paycheck of
$4,037.20 for one month, what was
the amount of sales for the month? Show work.
26. Let f (x) = 5x
2
– 4 and g(x) = x – 3.
(a) Find the composite function ))(( xgf o and simplify. Show
work.
(b) Find ( ) ( 1)f g −o . Show work.

19. 27. Find the exact solutions and simplify as much as possible:
3x
2
+ 2 = 8x. Show work.
28. Given the function
1
( ) 6
5
f x x= − , find a formula for the inverse function. Show work.
College Algebra MATH 107 Spring, 2016, V4.7
Page 11 of 11
29. Donut Delights, Inc. has determined that when x donuts are
made daily, the profit P, in
dollars, is given by
P(x) = –0.002 x
2
+ 4.7x – 1350
(a) What is the company’s profit if 800 donuts are made daily?

20. (b) How many donuts should be made daily in order to
maximize the company’s profit? Show
work.
30. Solve:
2
10 42
0
7 49
x
x x
−
+ =
− −
. Show work.
Math 107 Final ExaminationSpring, 20162
Math 107 College

21. AlgebraName______________________________
Final Examination: Spring, 2016Instructor
__________________________
Answer Sheet
Instructions:
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.
Record your answers and work in this document.
There are 30 problems.
Problems #1-12 are multiple choice. Record your choice for
each problem.
Problems #13-21 are short answer. Record your answer for
each problem.
Problems #22-30 are short answer with work required. When
requested, show all work and write all answers in the spaces
allotted on the following pages. You may type your work using
plain-text formatting or an equation editor, or you may hand-
write your work and scan it. In either case, show work neatly
and correctly, following standard mathematical conventions.
Each step should follow clearly and completely from the
previous step. If necessary, you may attach extra pages.
You must complete the exam individually. Neither
collaboration nor consultation with others is allowed. Your
exam will receive a zero grade unless you complete the
following honor statement.
Please sign (or type) your name below the following honor
statement:
I have completed this final examination myself, working
independently and not consulting anyone except the instructor. I
have neither given nor received help on this final examination.
Name _____________________Date___________________

22. MULTIPLE CHOICE. Record your answer choices.
1.7.
2.8.
3.9.
4.10.
5.11.
6.12.
SHORT ANSWER. Record your answers below.
13.
14.
15.
16.
17.
18.
19. (a)
(b)
(c)
20. (a)
(b)
(c)
(d)
21. (a)

23. (b)
(c)
(d)
SHORT ANSWER with Work Shown. Record your answers and
work.
Problem Number
Solution
22
Answers:
(a)
(b)
Work/for part (a) and explanation for part (b):

24. 23
Answers:
(a)
(b)
(c)
Work for part (a):

25. 24
Answer:
Work:
25
Answer:

26. Work:
26
Answers:
(a)
(b)
Work for part (a) and for part (b):

27. 27
Answer:
Work:

28. 28
Answer:
Work:

29. 29
Answers:
(a)
(b)
Work for (b):

30. 30
Answer:
Work: