I have attached the assignments and two answer sheets you can use. Please show all of your work neatly and write all of your answers on the Answer Sheet and if use an extra sheet of paper for solving problems please attach as well.

You may have to write steps of the solution or justify your answer to get credit. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan your work. 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. If you do the work by hand, please make sure that the scans include all of your work, are completely readable, and are submitted right-side up. Most scanners have a setting that will allow you to create one PDF document from all the pages of your Answer Sheet β please make use of this option if it is available on your scanner. You must submit a single file in commonly used formats, for example word processing or PDF.

Math 107 Final Exam Spring 2020

Professor: Dr. Kamal Hennayake

This is an open-book exam. You may only 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 β 12 are Multiple Choice. (Work not required to be shown)

Problems $13 β 25 are Short Answer. (Work not required to be shown)

Problems #26 β 30 are Short Answer with work required to be shown.

MULTIPLE CHOICE

1) Find the coordinates of the vertex of the graph of the function.

π(π₯) = β2π₯ 2 β 4π₯ + 8

A. (β1, 10)

B. (β1, 14)

C. (1, 2)

D. (10, β1)

E. (2, 1)

2) What is the end behavior of the graph?

A.

left -negative, right -positive

B.

left -positive, right βpositive

C.

left -negative, right βnegative

D.

left -positive, right -negative

3) Determine if the function is Odd, Even, or neither.

π(π₯) = β

A. Odd

B. Even

2

+ 4π₯

3π₯

C. Neither

Math 107

Final Exam

Page 2

4) What is the least possible degree of the polynomial graphed below?

A.

2

B.

3

C.

4

D.

5

E.

6

4) Select the choice that is a graph of the function.

π(π₯) = 6

π₯β1

(π₯ + 3)(π₯ β 2)

(A)

(B)

(C)

(D)

6) Solve the equation.

3π₯ = 81

A. 2

B. 3

C. 4

D. 5

Math 107

Final Exam

Page 3

7) Starting with the graph of π(π₯) = 7π₯ , write the equation of the graph that results from shifting f(x) 8 units to

the left.

A. π(π₯) = 7π₯+8

B. π(π₯) = 7π₯β8

C. π(π₯) = 7π₯ + 8

D. π(π₯) = 7π₯ β 8

E. π(π₯) = 8 β 7π₯

8) What is the number of real zeros of the polynomial graphed below?

A. 3

B. 4

C. 5

D. 6

E. 7

9) Match the function with its graph. π(π₯) = β2(π₯ + 1)2 + 5

A.

C.

B.

D.

Math 107

Final Exam

Page 4

10) Which of the following criteria must be true about a function in order for that function to have an inverse?

1

π β1 (π₯) = π(π₯)

i.

ii.

iii.

iv.

π(π β1 (π₯)) = π₯ and π β1 (π(π₯)) = π₯

The function passes the horizontal line test

The function is one-to-one

A. ii only

B. ii, iii, iv

C. ii, iii

D. i, ii, iii, and iv

11) Which of the following statements indicate when c is a zero of a polynomial function f(x)?

i)

ii)

iii)

iv)

c is the x-value of an x-intercept of π(π₯).

c is a solution to f(x) = 0; that is f(c) = 0.

c is the function value of f(0); that is, f(0) = c.

c produces a remainder of 0 when f(x) is divided by x β c; that if π(π₯) = (π₯ β π)π(π₯)

A. i, iii, iv

B. i, ii, iv

C. i, ii, iii, and iv

D. i, ii

12) Use the graph of the rational function to find the requested information.

As π₯ β 3β , π(π₯) β?

A.

β

B.

ββ

C.

0

D.

3

E.

β3

SHORT ANSWER (Work not required to be shown)

13) Give the domain of π(π₯) = 3 + 7β14 β 4π₯ in interval notation.

14) The point (β12, β18) is on the graph of π¦ = π(π₯)

1

a. A point on the graph of π¦ = π(π₯), where π(π₯) = 3 π(π₯) + 15

b. A point on the graph of π¦ = π(π₯), where π(π₯) = π(12 β π₯)

c. A point on the graph of π¦ = π(π₯), where π(π₯) = β2π(β3π₯)

15) Tell whether the vertex is a maximum or a minimum. π(π₯) = β10π₯ 2 β 81π₯ β 811

Math 107

Final Exam

Page 5

16) Consider the function graphed below. Answer the followings. Join multiple intervals with a union if

needed. For example: the domain of the function is (ββ, β).

a. Give the interval(s) where the function is increasing.

b. Give the interval(s) where the function is decreasing.

c. Give the interval(s) where the function is constant.

d. Give the range of the function using interval notation.

17) Complete the description of the piecewise function graphed below.

ππ

π(π₯) =

ππ

{

ππ

18) Consider the function π(π₯) = 102|π₯ + 2| β 20400 to find the intercepts.

a. Find the x-intercept(s) (if any as point(s)).

b. Find the y-intercept (if any as a point).

19) Determine an equation for the pictured graph. Write your answer in factored form. Do not expand the

equation.

20) Write an equation for a rational function with:

Vertical asymptotes at x = 6 and x = 5. The x intercepts at x = -5 and x = 3. Horizontal asymptote at y = 5

Math 107

Final Exam

Page 6

21) Solve the following quadratic inequality. βπ₯ 2 + π₯ β€ 132. Write your answer in interval notation.

1

22) Write log π 2 = β 2 in exponential form.

23) Solve the equation log π πβ21 = π₯ for x.

24) The number of bacteria in a culture is given by the function π(π‘) = 9050π 0.45π‘ . Where time is measured in

hours.

a. What is the relative rate of growth of this bacterium population?

b. What is the initial population of the culture?

c. How many bacteria will the culture contain in five days?

25) Given that π(π₯) = βπ₯ 2 + 5π₯ and π(π₯) = π₯ β 7 calculate the followings.

a. (π β π)(β5)

b. (π β π)(β5)

SHORT ANSWERS WITH WORK REQUERED TO BE SHOWN AS INDICATED.

26) Solve the equation for x? Show work clearly.

log 3 (π₯ + 3) = log 3 π₯ + log 3 3

27) The population of the world in 1987 was 5 billion and the relative growth rate was estimated at 2 percent

per year. Assuming that the world population follows an exponential growth model, find the projected world

population in 2025. Round your answer to 2 decimal places in billions. Show work clearly.

2

4

28) Let π(π₯) = π₯β3 and π(π₯) = π₯β5.

a. Find (π β π)(π₯) Show work clearly.

b. Find and the domain of (π β π)(π₯). Justify your answer.

29) Solve the rational inequality. Write your answer in interval notation. Show work clearly.

π₯β8

β€1

π₯+9

2π₯

30) Find the inverse function of π(π₯) = π₯+7. Show work clearly.

Math 107 Final Examination

Spring, 2020

1

Math 107 College Algebra

Name______________________________

Final Examination: Spring, 2020

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. Record your choice for each problem.

Problems #13-25 are short answer. Record your answer for each problem.

Problems #26-30 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.

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___________________

Math 107 Final Examination

Spring, 2020

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.

(a)

(b)

(c)

15.

16.

(a)

(b)

(c)

(d)

17.

(a)

(b)

(c)

(d)

(e)

(f)

18.

(a)

(b)

2

Math 107 Final Examination

19.

20.

21.

22.

23.

24.

(a)

(b)

(c)

25.

(a)

(b)

Spring, 2020

3

Math 107 Final Examination

Spring, 2020

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

Problem

Number

Solution

Answer:

Work:

26

Answer:

Work:

27

4

Math 107 Final Examination

Answers:

(a)

(b)

Work for part (a):

28

Justification for part (b):

Answer:

Work:

29

Answer:

Work:

30

Spring, 2020

5

Math 107 Final Examination

Spring, 2020

1

Math 107 College Algebra

Name______________________________

Final Examination: Spring, 2020

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. Record your choice for each problem.

Problems #13-25 are short answer. Record your answer for each problem.

Problems #26-30 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.

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___________________

Math 107 Final Examination

Spring, 2020

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.

(a)

(b)

(c)

15.

16.

(a)

(b)

(c)

(d)

17.

(a)

(b)

(c)

(d)

(e)

(f)

18.

(a)

(b)

2

Math 107 Final Examination

19.

20.

21.

22.

23.

24.

(a)

(b)

(c)

25.

(a)

(b)

Spring, 2020

3

Math 107 Final Examination

Spring, 2020

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

Problem

Number

Solution

Answer:

Work:

26

Answer:

Work:

27

4

Math 107 Final Examination

Answers:

(a)

(b)

Work for part (a):

28

Justification for part (b):

Answer:

Work:

29

Answer:

Work:

30

Spring, 2020

5