# Quiz 2

Math 107 Section 4060 – Quiz #2 – Due November 9, 2021 – page 1 of 4

Follow these directions carefully.

• This quiz is due by 11:59 Eastern time on November 9, 2021.

o This is an important assignment, counting 9% of your grade.

o Submit this assignment in your assignments folder by the due date.

• Answer all the questions. There are 23 problems on 4 pages.

o There are 100 points possible.

o No work is required for the MULTIPLE CHOICE SECTION or for the SHORT

ANSWER SECTION. There is no partial credit for these problems, so please

consider your answers carefully.

o Show all work for the LONG ANSWER SECTION. There is partial credit for

these problems

• Use the template provided to answer the MULTIPLE CHOICE and SHORT ANSWER

questions. Please use a separate document to answer the long answer section. You

may type up your answers in a document (like Word or Excel) or handwrite your

answers and scan them in – up to you.

• Submit your assignment as an attachment. Under no circumstances should you

type your answers into a text box.

MULTIPLE CHOICE QUESTIONS. (30 pts total, 3 pts each)

1. The distance between (0,3) and (0, −3) is:

A. 0 C. 9√2

B. 6 D. None of these

2. Consider the graph of the equation � = 3 + 2�!. Which one of the following is true?

A. It is not the graph of a function.

B. It is symmetric with respect to the origin.

C. It is symmetric about the x-axis.

D. It is symmetric about the y-axis.

3. Consider the graph of the equation � = 1 − �!. Which one of the following is true?

A. It is the graph of a function.

B. It is symmetric with respect to the origin.

C. It is symmetric about the x-axis.

D. It is symmetric about the y-axis.

5. The point (�, �) is in the second quadrant. In which quadrant is (−3�, 2�)?

A. I

B. II

C. III

D. IV

Math 107 Section 4060 – Quiz #2 – Due November 9, 2021 – page 2 of 4

6. Consider the following statements:

I. A horizontal line through the point (−3,2) has equation � = 2.

II. A vertical line through the point (√3, −5) has equation � = √3.

III. The relation {(0,8), (2,5), (−2,8), (1,5)} is a function.

Which of the statements are true?

A. All of them are true.

B. I only.

C. II only.

D. III only.

7. Consider the function �(�) = �! − 9. The domain of 1/� is:

A. (−∞, −3) ∪ (3, ∞)

B. (−∞, −3) ∪ (−3,3) ∪ (3, ∞)

C. (−3,3)

D. (−∞, ∞)

8. Consider the function �(�) = ”

√$%!

. Its domain is:

A. [0, ∞)

B. [2, ∞)

C. (0, ∞)

D. (2, ∞)

9. Consider the functions �(�) = �! − 9 and �(�) = √� − 2. The domain of

(�/�)(�) is:

A. [2, ∞) C. (−∞, −3) ∪ (−3,3) ∪ (3, ∞)

B. [2,3) ∪ (3, ∞) D. (−∞, −3) ∪ (−3,2) ∪ (2, ∞)

10. Consider the function �(�) = �&!. Consider the following statements:

I. f is an odd function.

II. The graph of f is symmetric about the origin.

Which of the statements are true?

A. I is true, but not II.

B. II is true, but not I.

C. I and II are both true.

D. Neither statement is true.

Math 107 Section 4060 – Quiz #2 – Due November 9, 2021 – page 3 of 4

SHORT ANSWER QUESTIONS. (30 pts total, 3 pts each)

11. If the graph of a relation is symmetric about the x-axis and the point (−4,7) is on the

graph of the relation, what other point must be on the graph of the relation?

12. If the graph of a relation is symmetric about the y-axis and the point (−4, −7) is on

the graph of the relation, what other point must be on the graph of the relation?

13. If the graph of a relation is symmetric about the origin and the point (3, −2) is on

the graph of the relation, what other point must be on the graph of the relation?

14. Suppose that �(�) = � − 3 and �(�) = 9 − �!. Find (� − �)(−3).

15. Suppose that �(�) = � − 3 and �(�) = 9 − �!. Determine the domain of the

quotient function ℎ(�) = ‘($)

*($) and express the answer in interval notation.

16. Suppose that �(�) = −�! − 2� − 6. Determine �(−3�) and simplify.

Questions 17 and 18 involve the following function defined piecewise:

�(�) = A 1 − 2�! for � ≤ −2

−|� + 2| for � > −2

17. Find �(0).

18. Find �(−2).

Questions 19, and 20 refer to this number line:

19. What is the x-coordinate of A?

20. What is the (straight-line) distance between A and B?

Math 107 Section 4060 – Quiz #2 – Due November 9, 2021 – page 4 of 4

LONG ANSWER PROBLEMS. (40 pts total)

21. Consider the points in the plane defined by �(4, −4) and �(−2, −1).

a. Find the midpoint of ��. (5pts)

b. Find the length of �� and express the answer in simplest radical form.

(10 pts)

c. When �� is reflected about the y-axis, what are the endpoints of the resulting

line segment? (5 pts)

22. Consider the graph of the equation 5� − 2� = 15.

a. Find the (x, y) coordinates of the intercept(s), if any. (5 pts)

b. Write y as a function of x by solving for y. (5 pts)

c. Make a table of values where � = −3, −2, −1, 0, 1, 2, 3 and then graph the

line. (5 pts)

23. Graph the relation {(0,8), (2,5), (−2,8), (−2,5), (1,5), (2,7)}. State its domain and

range. (5 pts)