Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each value in the domain is paired with exactly one value in the range.

Question 2

Given the set of ordered pairs $$\{(2,3), (2,4), (3,5)\}$$, is this relation a function? What is its domain?

Accepted Answer

No, not a function; Domain = $$\{2, 3\}$$

Question 3

Given the set of ordered pairs $$\{(1,3), (2,3), (3,5)\}$$, is this relation a function? What is its range?

Accepted Answer

Yes, it is a function; Range = $$\{3, 5\}$$

Question 4

Refer to the first image (circle with vertical lines). Does the graph represent $$y as a $$function of $$x$$?

Accepted Answer

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

Question 5

Refer to the second image (parabola with vertical lines). Does the graph represent $$y as a $$function of $$x$$?

Accepted Answer

Yes, because no vertical line intersects the graph more than once.

Question 6

Given $$f(x) = -3x + 1$$, what is $$f(3)$$?

Accepted Answer

$$-8$$

Question 7

Given $$f(x) = -3x + 1$$, what is $$f(A)$$?

Accepted Answer

$$-3A + 1$$

Question 8

Suppose $$f is a $$function such that $$f(-2) = 1$$, $$f(2) = 5$$, $$f(4) = 6$$, $$f(8) = 9. $$What is the domain of $$f$$?

Accepted Answer

$$\{-2, 2, 4, 8\}$$

Question 9

Suppose $$f is a $$function such that $$f(-2) = 1$$, $$f(2) = 5$$, $$f(4) = 6$$, $$f(8) = 9. $$What is the range of $$f$$?

Accepted Answer

$$\{1, 5, 6, 9\}$$

Question 10

What is the domain of the function $$f(x) = \dfrac{2x+6}{x+9}$$?

Accepted Answer

All real numbers except $$x = -9$$

Question 11

What is the domain of the function $$f(x) = 3x^2$ - 5x + 1$$?

Accepted Answer

All real numbers

Question 12

Refer to the third image (parabola opening upwards). What is the domain and range of the function shown?

Accepted Answer

Domain: $$(-\infty, \infty)$$; Range: $$[2, \infty)$$

Question 13

Refer to the fourth image (piecewise graph). What is $$f(2)$$?

Accepted Answer

$$1$$

Question 14

Refer to the fourth image (piecewise graph). What is $$f(-3)$$?

Accepted Answer

$$-3$$

Question 15

Which of the following statements about the vertical line test is correct?

Accepted Answer

A graph represents a function if and only if no vertical line intersects the graph more than once.

Question 16

If a function $$f(x) is $$defined by a formula with a denominator, what must you do to find its domain?

Accepted Answer

Exclude all $$x$$ values that make the denominator zero.

Question 17

Which of the following real-life scenarios can be modeled by a function?

Accepted Answer

Assigning each person in a class their unique student ID number.

Functions and Their Representations: Study Guide for College Algebra

Study Guide - Practice Questions