Question 1

Which of the following relations is a function?

Accepted Answer

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

Question 2

Given the equation $y = -2x + 10$, is this a function? If so, what is $f(3)$?

Accepted Answer

Yes, $f(3) = 4$

Question 3

Which graph passes the Vertical Line Test and represents a function?

Accepted Answer

A parabola opening upwards

Question 4

What is the domain of the function $f(x) = \sqrt{x+4}$?

Accepted Answer

$[-4, \infty)$

Question 5

Find the domain of $f(x) = \frac{1}{x^2 - 5x + 6}$.

Accepted Answer

$(-\infty, 2) \cup (2, 3) \cup (3, \infty)$

Question 6

Which of the following equations is NOT a function?

Accepted Answer

$x^2 + y^2 = 25$

Question 7

Given the graph of $f(x)$ with domain $[-4, 5]$ and range $[-2, 6]$, which interval notation correctly expresses the range?

Accepted Answer

$[-2, 6]$

Question 8

If $f(x) = \sqrt{x}$, what is the restriction on $x$ for the domain?

Accepted Answer

$x \geq 0$

Question 9

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

Accepted Answer

$f(-2) = 15$

Question 10

Which of the following is the correct interval notation for the domain of $f(x) = \frac{1}{x-2}$?

Accepted Answer

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

Question 11

Given the relation $\{(1,2), (2,3), (3,4), (2,5)\}$, is this a function?

Accepted Answer

No, because the input 2 maps to two different outputs

Question 12

If the graph of a relation fails the Vertical Line Test, what does this mean?

Accepted Answer

The relation is not a function

Question 13

What is the range of $f(x) = x^2$ for $x$ in $[-2, 3]$?

Accepted Answer

$[0, 9]$

Question 14

Which of the following is the correct set builder notation for the domain of $f(x) = \sqrt{x+4}$?

Accepted Answer

$\{x \mid x \geq -4\}$

Question 15

For the function $f(x) = \frac{2x+1}{x-3}$, what value of $x$ is excluded from the domain?

Accepted Answer

$x = 3$

Question 16

If $f(x) = \sqrt{x-2}$, what is $f(6)$?

Accepted Answer

$f(6) = 2$

Question 17

Which of the following is NOT a valid interval notation for a domain?

Accepted Answer

$[5, -2]$

Question 18

Given $f(x) = x^2$ and $g(x) = x + 2$, what is $f(g(2))$?

Accepted Answer

$f(g(2)) = 16$

Question 19

If $f(x) = \frac{1}{x}$, what is the domain of $f$?

Accepted Answer

$(-\infty, 0) \cup (0, \infty)$

Question 20

Which of the following statements about functions is TRUE?

Accepted Answer

A function assigns exactly one output to each input

Relations, Functions, and Domain & Range in College Algebra

Study Guide - Practice Questions