Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each input is paired with at most one output.

Question 2

Given the relation $\{(-3, 5), (0, 2), (3, 5)\}$, what is the domain?

Accepted Answer

$\{-3, 0, 3\}$

Question 3

Which of the following relations is NOT a function?

Accepted Answer

$\{(2, 5), (0, 2), (2, 9)\}$

Question 4

What is the range of the relation $\{(-4, 2), (-2, -1), (1, 2), (3, 4)\}$?

Accepted Answer

$\{2, -1, 4\}$

Question 5

Which graph passes the vertical line test and represents a function?

Accepted Answer

A graph where every vertical line intersects the curve at most once.

Question 6

Given the function $f(x) = 3x - 1$, what is $f(4)$?

Accepted Answer

$11$

Question 7

If a function is defined as $f(x) = x^2$, what is the domain and range?

Accepted Answer

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

Question 8

Which of the following is the correct function notation for the equation $y = 3x - 1$?

Accepted Answer

$f(x) = 3x - 1$

Question 9

If $g(x) = x + 2$ and $f(x) = 2x$, what is $(f \circ g)(3)$?

Accepted Answer

$10$

Question 10

Which of the following best describes the domain of the square root function $f(x) = \sqrt{x}$?

Accepted Answer

Domain: $[0, \infty)$

Question 11

Given the function $f(x) = x^3$, what is the range?

Accepted Answer

$(-\infty, \infty)$

Question 12

If $f(x) = x^2$ and $g(x) = x + 1$, what is $(f \circ g)(2)$?

Accepted Answer

$9$

Question 13

Which of the following is NOT a valid way to represent a relation?

Accepted Answer

As a single number

Question 14

If a relation is given by the set $\{(1, 2), (2, 3), (3, 4), (4, 5)\}$, what is the range?

Accepted Answer

$\{2, 3, 4, 5\}$

Question 15

Which of the following statements about the cube root function $f(x) = \sqrt[3]{x}$ is true?

Accepted Answer

The domain and range are both $(-\infty, \infty)$.

Question 16

If $f(x) = x^2$ and $g(x) = 2x + 1$, what is $(g \circ f)(2)$?

Accepted Answer

$9$

Question 17

Which of the following is a real-world example of a function?

Accepted Answer

A vending machine where each button dispenses exactly one snack.

Question 18

If $f(x) = x^2$ and $g(x) = \sqrt{x}$, what is the domain of $(g \circ f)(x)$?

Accepted Answer

Domain: $(-\infty, \infty)$

Question 19

If $f(x) = x + 1$ and $g(x) = x^2$, what is $(f \circ g)(2)$?

Accepted Answer

$5$

Relations and Functions: Beginning-Intermediate Algebra Study Guide

Study Guide - Practice Questions