Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

Given the set of ordered pairs $$\{(1, 2), (2, 3), (1, 4)\}$$, is this a function?

Accepted Answer

No, because the input 1 is paired with two different outputs.

Question 3

Which of the following graphs passes the vertical line test and represents a function?

Accepted Answer

A graph where no vertical line intersects the graph more than once.

Question 4

Given the equation $$y^2 = x + 3$, is this a function?

Accepted Answer

No, because for some values of $$x$$, there are two possible values of $$y.$$

Question 5

What is the domain of the function $$f(x) = \sqrt{x - 2}$$?

Accepted Answer

$$[2, \infty)$$

Question 6

What is the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 7

Given the relation $$\{(2, 5), (3, 7), (4, 5)\}$$, what are the inputs and outputs?

Accepted Answer

Inputs: $$\{2, 3, 4\}$$; Outputs: $$\{5, 7\}$$

Question 8

Rewrite $$y = 2x + 1 in $$function notation and evaluate at $$x = 3.$$

Accepted Answer

$$f(x) = 2x + 1$$, $$f(3) = 7$$

Question 9

Which of the following is the correct interval notation for all real numbers except $$x = 2$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 10

If $$f(x) = x^2$ - 4$$, what is the range of $$f(x)$$?

Accepted Answer

$$[-4, \infty)$$

Question 11

Which of the following equations is NOT a function?

Accepted Answer

$$x^2$$ + $$y^2 = 9$

Question 12

Given the graph of $$y = x^2$, what is the domain and range?

Accepted Answer

Domain: $$(-\infty, \infty)$$; Range: $$[0, \infty)$$

Question 13

Which of the following best describes the vertical line test?

Accepted Answer

A graph is a function if no vertical line intersects it more than once.

Question 14

Find the domain of $$f(x) = \sqrt{7 - x}.$$

Accepted Answer

$$(-\infty, 7]$$

Question 15

If $$f(x) = \frac{1}{x^2$ - 9}$$, what is the domain?

Accepted Answer

$$(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$$

Question 16

Given the equation $$y = x^2$ + 2x + 1$$, rewrite it in function notation and evaluate at $$x = -1.$$

Accepted Answer

$$f(x) = x^2$ + 2x + 1$$, $$f(-1) = 0$$

Question 17

Which of the following is the correct set builder notation for the domain $$[2, 5)$$?

Accepted Answer

$$\{x \mid 2 \leq x \u003c 5\}$$

Question 18

If a function has a domain of $$(-\infty, 4]$$ and a range of $$[0, \infty)$$, which of the following could be its graph?

Accepted Answer

A parabola opening upwards with vertex at $$(4, 0)$$

Question 19

Which of the following is NOT a valid way to express the domain of a function?

Accepted Answer

As a list of all possible $$y-$$values.

Introduction to Functions and Their Graphs: Relations, Functions, Domain, and Range

Study Guide - Practice Questions