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

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