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.

College Algebra MATH 107 Spring, 2019, V4.2

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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= −

College Algebra MATH 107 Spring, 2019, V4.2

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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

College Algebra MATH 107 Spring, 2019, V4.2

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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: ________

College Algebra MATH 107 Spring, 2019, V4.2

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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

College Algebra MATH 107 Spring, 2019, V4.2

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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.

College Algebra MATH 107 Spring, 2019, V4.2

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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.

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