Question 1

Which of the following is the correct interval notation for the set of all real numbers $$x$$ such that $$x \u003e -2$$?

Accepted Answer

$$(-2, \infty)$$

Question 2

Given the mapping diagram below, what is the domain of the relation?

[See image 3]

Accepted Answer

$$\{-2, 1, 3\}$$

Question 3

Which of the following best describes a function?

Accepted Answer

A relation in which each element in the domain corresponds to exactly one element in the range.

Question 4

Given the graph below, what is the range of the relation?

[See image 2]

Accepted Answer

$$\{5, 2, -2, 1\}$$

Question 5

Which of the following relations is NOT a function? Use the vertical line test to decide.

A. [See image 5]
B. [See image 6]
C. [See image 7]
D. [See image 8]

Accepted Answer

D. [See image 8]

Question 6

Given the mapping diagram below, is the relation a function?

[See image 9]

Accepted Answer

Yes, because each element in the domain is paired with exactly one element in the range.

Question 7

If $$f(x) = x^2$ - 2x + 1$$, what is $$f(3)$$?

Accepted Answer

Question 8

Given the graph below, use function notation to find $$f(3)$$.

[See image 11]

Accepted Answer

$$4$$

Question 9

Which of the following is the correct set-builder notation for the interval $$(-\infty, 5]$$?

Accepted Answer

$$\{x \mid x \leq 5\}$$

Question 10

A real-world scenario: The temperature $$T (in $$degrees Celsius) at time $$t (in $$hours) is given by $$T(t) = 20 - 2t. $$What is the temperature after 5 hours?

Accepted Answer

$$10$$ degrees Celsius

Question 11

Given the relation $$\{(2, 3), (4, 5), (2, 6)\}$$, is this relation a function?

Accepted Answer

No, because the input $$2 is $$paired with two different outputs.

Question 12

Which of the following graphs represents a function? (Use the vertical line test)

A. [See image 4]
B. [See image 7]
C. [See image 8]
D. [See image 1]

Accepted Answer

B. [See image 7]

Question 13

If $$f(x) = 2x + 1$$, what is the value of $$f(-3)$$?

Accepted Answer

$$-5$$

Question 14

Which of the following best describes the range of the function $$f(x) = x^2$ for all real numbers x$?

Accepted Answer

$$[0, \infty)$$

Question 15

Given the mapping diagram below, which element in the range is paired with more than one element in the domain?

[See image 9]

Accepted Answer

$$5$$

Question 16

Suppose $$f(x) = x - 2. $$What is the domain and range of $$f$$?

Accepted Answer

Both the domain and range are the set of all real numbers.

Question 17

Which of the following is NOT a correct way to write the set of all real numbers greater than or equal to $$3$$?

Accepted Answer

$$(-\infty, 3]$$

Question 18

A chemical reaction's rate $$R (in $$mol/L/s) as a function of temperature $$T (in$$ $$^\circC) is $$given by $$R(T) = 0.5T + 2. $$What is the rate when $$T = 10$$?

Accepted Answer

$$7$$ mol/L/s

Question 19

Given the graph of a circle centered at the origin, does it represent a function? (Use the vertical line test)

[See image 8]

Accepted Answer

No, because a vertical line can intersect the graph at more than one point.

Section 1.2: Introduction to Relations and Functions

Study Guide - Practice Questions

Study Guide - Flashcards