Pleaseplease see the attached algebra quiz. Show work when necessary. Answers must be done in the word document. If it’s late I will withdraw.

College Algebra MATH 107

Fall, 2019, V1.21

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. ______

4

2

-4

2

-2

4

-2

-4

A.

B.

C.

D.

Domain [–1, 1];

Domain [–2, 2];

Domain [–3, –1];

Domain [–3, 1];

2. Solve:

A.

B.

C.

D.

x + 17 = x − 3

Range [–2, 0]

Range [–3, 1]

Range [0, 2]

Range [–2, 2]

2. ______

No solution

−1

8

−1, 8

Page 1 of 11

College Algebra MATH 107

Fall, 2019, V1.21

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

A.

(1, 5)

B.

(– 0.5, 3)

C.

(− ,

D.

(–2, 2)

3. ______

− 0.5) and (5, 6.5)

4. Determine whether the graph of y = x + 8 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: | 7 – 5x | 8.

A.

B.

C.

D.

5. ______

[– 1/5, )

[– 1/5, 3]

(–, –1/5]

(–, –1/5] [3, )

Page 2 of 11

College Algebra MATH 107

Fall, 2019, V1.21

6. Which of the following represents the graph of 7x − 2y = 14 ?

A.

B.

C.

D.

6. ______

Page 3 of 11

College Algebra MATH 107

Fall, 2019, V1.21

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.

y = −8x +123

B.

1

y = − x −3

8

C.

1

y = x−5

8

D.

1

y = x−7

8

8. Which of the following best describes the graph?

A.

B.

C.

D.

8. ______

It is an absolute value relation.

It is not the graph of a function.

It is the graph of a function but not one-to-one

It is the graph of a function and it is one-to-one.

Page 4 of 11

College Algebra MATH 107

9. Express as an equivalent expression: log (x + 4) – 2 log y + log 1

A.

log ( x + 5 − 2 y )

B.

log( x + 4)

log( y 2 )

C.

x+4

log 2

y

D.

x+5

log

2y

10. Which of the functions corresponds to the graph?

Fall, 2019, V1.21

9. ______

10. ______

A. f ( x ) = e− x + 3

B. f ( x ) = −e x + 3

C. f ( x ) = e− x + 4

D. f ( x ) = e x + 4

Page 5 of 11

College Algebra MATH 107

Fall, 2019, V1.21

11. Suppose that a function f has no x-intercepts.

Which of the following statements MUST be true?

A.

B.

C.

D.

11. ______

f is an invertible function.

The equation f (x) = 0 has no real-number solution.

The graph of f has no points whose x-coordinate is 0.

The graph of f is a horizontal line.

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. ______

-4

4

4

2

2

2

-2

4

-4

2

-2

-2

-2

-4

-4

y = f (x)

4

y = g(x)

A.

B.

C.

D.

g(x) = f (x – 1) – 2

g(x) = f (x + 1) – 2

g(x) = f (x + 1) – 1

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

Page 6 of 11

College Algebra MATH 107

Fall, 2019, V1.21

SHORT ANSWER:

13. Multiply and simplify: (3 + 4i)(7 – 2i).

Write the answer in the form a + bi, where a and b are real numbers.

14. Solve, and write the answer in interval notation:

x −1

0.

x−6

Answer: ________

Answer: ________

15. A bowl of soup at 195 F. is placed in a room of constant temperature of 65 F. The

temperature T of the soup t minutes after it is placed in the room is given by

T(t) = 65 + 130 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: ________

1

16. Find the value of the logarithm: log 4 .

16

17. Solve:

85 x+8 = 64

.

Answer: ________

Answer: ________

18. Suppose $7,000 is invested in an account at an annual interest rate of 3.5% 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 + 6x + 14.

(a) Find the vertex.

Answer: ________

(b) State the range of the function.

Answer: ________

(c) On what interval is the function increasing?

Answer: ________

Page 7 of 11

College Algebra MATH 107

Fall, 2019, V1.21

20. Consider the polynomial P(x), shown in both standard form and factored form.

1

9

19

9

1

P( x) = x 4 + x3 + x 2 − x − 2 = ( x + 5)( x + 4)( x + 1)( x − 1)

10

10

10

10

10

(a) Which sketch illustrates the end behavior of the polynomial function?

A.

B.

vvvv

C.

vvvv

D.

vvvv

vvvv

Answer: ________

(b) State the zeros of the function.

Answer: ________________

(c) State the y-intercept.

Answer: ________________

Answer: ________

(d) State which graph below is the graph of P(x).

GRAPH A

GRAPH B

GRAPH C

GRAPH D

Page 8 of 11

College Algebra MATH 107

21. Let f ( x) =

Fall, 2019, V1.21

3x 2 − 3

.

x2 − 4

(a) State the domain.

Answer: _________________

(b) State the vertical asymptote(s).

Answer: _________________

(c) State the horizontal asymptote.

Answer: _________________

(d) Which of the following represents the graph of f ( x) =

3x 2 − 3

?

x2 − 4

GRAPH A.

GRAPH B.

GRAPH C.

GRAPH D.

Answer: ______________

Page 9 of 11

College Algebra MATH 107

Fall, 2019, V1.21

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

22. Let f (x) = x – 8 and g ( x) =

x+3.

f

(a) Find (−2) . Show work.

g

(b) Find the domain of the quotient function

f

. Explain.

g

23. Points (–5, 9) and (1, 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 (–9, 7) and (–6, 4). Write the

equation in slope-intercept form. Show work.

25. Dan, a resident of Metropolis, pays Metropolis an annual tax of $45 plus 2.7% of his annual

income. If Dan paid $2,016 in tax, what was Dan’s income? Show work.

26. Let f (x) = 4×2 – 5 and g(x) = x – 2.

(a) Find the composite function ( f g )(x) and simplify. Show work.

(b) Find ( f o g ) (−3) . Show work.

27. Find the exact solutions and simplify as much as possible: 3×2 = 8 + 8x. Show work.

28. Given the function f ( x) =

1

x − 4 , find a formula for the inverse function. Show work.

7

Page 10 of 11

College Algebra MATH 107

Fall, 2019, V1.21

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 + 27.50x – 150

(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:

x −3

20

= 2

. Show work.

x+2 x −4

Page 11 of 11

Math 107 Final ExaminationFall, 20191

Math 107 College Algebra

Name______________________________

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 plaintext 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.

Math 107 Final ExaminationFall, 20192

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)

Math 107 Final ExaminationFall, 20193

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

Problem

Number

Solution

Answers:

(a)

(b)

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

22

Answers:

(a)

(b)

(c)

Work for part (a):

23

Math 107 Final ExaminationFall, 20194

Answer:

Work:

24

Answer:

Work:

25

Answers:

(a)

(b)

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

26

Math 107 Final ExaminationFall, 20195

Answer:

Work:

27

Answer:

Work:

28

Math 107 Final ExaminationFall, 20196

Answers:

(a)

(b)

Work for (b):

29

Answer:

Work:

30