Question 1

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$\{(1, 4), (2, 4), (3, 4)\}$

Question 2

Given the function $f(x) = 2x^2 - x + 3$, what is $f(-7)$?

Accepted Answer

$108$

Question 3

Which of the following relations is NOT a function?

Accepted Answer

$\{(4, 2), (5, 3), (4, 7)\}$

Question 4

If $f(x) = \sqrt{x+4}$, what is the domain of $f$?

Accepted Answer

$x \geq -4$

Question 5

A graph passes the vertical-line test if:

Accepted Answer

No vertical line intersects the graph more than once.

Question 6

Given $h(x) = \dfrac{3x+7}{x^2+2x-3}$, which values are NOT in the domain?

Accepted Answer

$x = -3$ and $x = 1$

Question 7

If $f(x) = x^2 - 6$, what is the range of $f$?

Accepted Answer

$[-6, \infty)$

Question 8

Which statement best describes the difference between a relation and a function?

Accepted Answer

A function assigns exactly one output to each input, while a relation may assign multiple outputs to an input.

Question 9

Given $f(x) = \dfrac{1}{x-3}$, which of the following statements is true?

Accepted Answer

$f(3)$$ does not exist because it results in division by zero.

Question 10

A hospital records the temperature of a patient every hour. Which of the following best describes the relationship between time and temperature?

Accepted Answer

It is a function because each hour has exactly one recorded temperature.

Question 11

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

Accepted Answer

$6$

Question 12

Which of the following is the correct notation for the value of a function $f$ at $x$?

Accepted Answer

$f(x)$

Question 13

Given the relation $\{(1, 2), (2, 3), (1, 4)\}$, what is the domain?

Accepted Answer

$\{1, 2\}$

Question 14

A function $f$ is defined by $f(x) = 2x^2 - x + 3$. What is $f(a-4)$?

Accepted Answer

$2a^2 - 17a + 39$

Question 15

Which of the following graphs could NOT represent a function?

Accepted Answer

A graph where a vertical line crosses the graph at two points.

Question 16

If $f(x) = \sqrt{x+4}$, what is the range of $f$?

Accepted Answer

$[0, \infty)$

Question 17

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

Accepted Answer

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

Question 18

Given $f(x) = x^2 - 5$, what is $f(3)$?

Accepted Answer

$4$

Question 19

If $f(x) = \dfrac{1}{x-3}$, which of the following is in the domain of $f$?

Accepted Answer

$x = -3$

Functions and Graphs: Fundamental Concepts and Applications

Study Guide - Practice Questions