# Determine the domain and range of the piecewise function. 1. ______

MATH 107 Final Exam Answers

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

Determine the domain and range of the piecewise function. 1. ______

4 2

-4 -2 2 4

-2 -4

Domain [–3, 3]; Range [–2, 4]

Domain [–3, 3]; Range [0, 3]

Domain [–2, 4]; Range [–3, 3]

Domain [–1, 4]; Range [–2, 2]

Solve: 2x+ 20= x+ 6 2. ______

−8,−2

−2

−14

No solution

Page 1 of 11

College Algebra MATH 107 Spring, 2016, V1.7

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

(–3.6, 0) and (6.7,∞)

(–2, 4)

(–∞, –2) and (4,∞)

(–1, 3)

4. Determine whether the graph of y= x−7 is symmetric with respect to the origin,

the x-axis, or the y-axis. 4. ______

symmetric with respect to the x-axis only

symmetric with respect to the y-axis only

symmetric with respect to the origin only

not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and not symmetric with respect to the origin

Solve, and express the answer in interval notation: | 5 – 6x|≥13. 5. ______

[4/3,∞)

(–∞,−4/3]∪ [3,∞)

(–∞, 3]∪ [−4/3,∞)

[–4/3, 3]

Page 2 of 11

College Algebra MATH 107 Spring, 2016, V1.7

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

B.

D.

Page 3 of 11

College Algebra MATH 107 Spring, 2016, V1.7

Write a slope-intercept equation for a line parallel to the line x + 3y = 8 which passes through the point (– 4, 5). 7. ______

y=−1 x+11

3 3

y=−1 x+5

3

y=1 x+5

3

y=−3x−7

Which of the following best describes the graph? 8. ______

It is the graph of an absolute value relation.

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.

It is not the graph of a function.

Page 4 of 11

College Algebra MATH 107 Spring, 2016, V1.7

9. Express as a single logarithm: 3 log (x + 2) + log 1 – log y 9. ______

A. 6 log( x)+1

log y

3 + 8

B. log x

y

C. log ( x+2)3

y

D. log(3 x+ 7− y)

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

f( x)= ex +3

f( x)= e−x +3

f( x)= e−x +2

f( x)=− ex +3

Math 107 College Algebra Name______________________________

Final Examination: Fall, 2015 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 #13-21 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___________________