CollegeAlgebra MATH 107 Spring, 2013, V2.2

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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 [–2, 1]; Range [–2, 4]

B. Domain [–2, 4]; Range [–3, 3]

C. Domain [–3, 0]; Range [0, 4]

D. Domain [–3, 3]; Range [–2, 4]

2. Solve: 15 2 6x x− = − 2. ______

A. 3

B. 9

C. 3, 7

D. No solution

2

4

–

4

-2

-4

2

4

-2

College Algebra MATH 107 Spring, 2013, V2.2

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3. Determine the interval(s) on which the function is increasing. 3. ______

A. (–∞, 3)

B. (–∞, – 2.5) and (1, 4.5)

C. (– 1, 3)

D. (– 2, 2)

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 x-axis only

B. symmetric with respect to the y-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: | 5 – 6x | ≤ 13. 5. ______

A. (–∞, −4/3] ∪ [3, ∞)

B. (–∞, –4/3]

C. [3, ∞)

D. [–4/3, 3]

College Algebra MATH 107 Spring, 2013, V2.2

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6. Which of the following represents the graph of 9x − 2y = 18 ? 6. ______

A. B.

C. D.

College Algebra MATH 107 Spring, 2013, V2.2

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7. Write a slope-intercept equation for a line parallel to the line x – 8y = 3 which passes through

the point (16, –5). 7. ______

A.

1

7

8

y x= −

B.

1

5

8

y x= −

C.

1

3

8

y x= − −

D. 8 123y 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.

College Algebra MATH 107 Spring, 2013, V2.2

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9. Express as a single logarithm: log x + log 1 – 4 log y 9. ______

A. ( )log 1 4x y+ −

B.

4

1

log

x

y

+

C.

4

log

x

y

D.

4

1

log

x

y

+

10. Which of the functions corresponds to the graph? 10. ______

A. ( ) 3xf x e= − +

B. ( ) 2xf x e−= +

C. ( ) 3xf x e−= +

D. ( ) 3xf x e= +

College Algebra MATH 107 Spring, 2013, V2.2

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11. The percentage score on a test varies directly as the number of correct responses. Julie

answered 21 questions correctly and earned a score of 70%. What would Julie’s percentage score

have been if she had answered 24 questions correctly? 11. ______

A. 73%

B. 77%

C. 80%

D. 96%

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) – 2

B. g(x) = f (x – 2) – 1

C. g(x) = f (x + 2) – 1

D. g(x) = f (x + 2) + 2

2 4 -2 -4

-2

-4

2

4

2 4 -2 -4

-2

-4

2

4

College Algebra MATH 107 Spring, 2013, V2.2

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SHORT ANSWER:

13. Multiply and simplify: (2 + 9i)(3 + 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:

8

0

1

x

x

+

≤

+

. Answer: ________

15. A bowl of soup at 180° 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 + 110 e

– 0.075 t

Find the temperature of the soup 26 minutes after it is placed in the room. (Round to the nearest

degree.)

Answer: ________

16. Find the value of the logarithm: 7

1

log

49

. Answer: ________

17. Solve:

5 96 36x − = . Answer: ________

18. Suppose $7,500 is invested in an account at an annual interest rate of 4.3% 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

+ 12x + 10.

(a) Find the vertex. Answer: ________

(b) State the range of the function. Answer: ________

(c) On what interval is the function increasing? Answer: ________

College Algebra MATH 107 Spring, 2013, V2.2

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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, 2013, V2.2

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21. Let

2

( )

3

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

2

( )

3

x

f x

x

+

=

−

? Answer: ______________

GRAPH A. GRAPH B.

GRAPH C. GRAPH D.

College Algebra MATH 107 Spring, 2013, V2.2

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SHORT ANSWER, with work required to be shown, as indicated.

22. Simplify:

( )

6

2 5 12 3

7

2a b a

b

b

−

−

−

. Show work.

23. Points (3, 1) and (–5, 9) 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 of the circle?

(c) What is the equation of the circle?

24. Find the equation for a line which passes through the points (6, –2) and (9, –8). Write the

equation in slope-intercept form. Show work.

25. Keith, a resident of Metropolis, pays Metropolis an annual tax of $40 plus 1.8% of his annual

income. If Keith paid $706 in tax, what was Keith’s income? Show work.

26. Let f (x) = 9x

2

+ 8 and g(x) = x – 1.

(a) Find the composite function ))(( xgf � and simplify. Show work.

(b) Find ( ) ( 2)f g −� . Show work.

27. Find the exact solutions and simplify as much as possible: 32x

2

+ 1 = 8x. Show work.

28. Given the function

1

( ) 8

4

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 is given

by

P(x) = –0.002 x

2

+ 4.6x – 1500

(a) What is the company’s profit if 700 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

7 24

0

4 16

x

x x

−

+ =

− −

. Show work.

Math 107 Final Examination

Spring, 2013 2

**Math 107 College Algebra**

** Name______________________________**

Final Examination: Spring, 2013 Instructor __________________________

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

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 st. 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 ep. 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___________________

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)

(b)

(c)

(d)

SHORT ANSWER with Work Shown. Record your answers and work.

Problem Number

Solution

22

Answer:

Work:

23

Answers:

(a)

(b)

(c)

Work for part (a):

24

Answer:

Work:

25

Answer:

Work:

26

Answers:

(a)

(b)

Work for part (a) and for part (b):

27

Answer:

Work:

28

Answer:

Work:

29

Answers:

(a)

(b)

Work for (b):

30

Answer:

Work:

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