Question 1

Which of the following best describes the domain of a function?

Accepted Answer

The set of all input numbers of the function.

Question 2

Given $f(x) = \dfrac{x(x-1)}{x-2}$ and $g(x) = x^2$, which of the following statements is true about their equality?

Accepted Answer

They are not equal for any $x$.

Question 3

What is the range of the function $f(x) = 3x^2 + 5$?

Accepted Answer

$[5, \infty)$

Question 4

Find the domain of $f(x) = \dfrac{x}{x^2 - x - 2}$.

Accepted Answer

$x 
eq 2$ and $x 
eq -1$

Question 5

Given $g(x) = \sqrt{2x-1}$, what is the domain of $g$?

Accepted Answer

$x \geq \dfrac{1}{2}$

Question 6

If $f(x) = x^2$, what is the difference quotient $\dfrac{f(x+h) - f(x)}{h}$?

Accepted Answer

$2x + h$

Question 7

For $f(x) = \dfrac{x}{3}$, compute the difference quotient $\dfrac{f(x+h) - f(x)}{h}$.

Accepted Answer

$\dfrac{1}{3}$

Question 8

Which of the following is NOT a correct definition according to the study materials?

Accepted Answer

Domain: The set of all output numbers is the domain of the function.

Question 9

Suppose $f(x) = x^2$ and $g(x) = x^2$ for all $x$ in $\mathbb{R}$. Are $f$ and $g$ equal?

Accepted Answer

Yes, because their domains and outputs are identical.

Question 10

A medical researcher models the dosage of a drug by $d(t) = \dfrac{t}{t-5}$, where $t$ is time in hours. What is the domain of $d$?

Accepted Answer

$t 
eq 5$

Question 11

If $f(x) = \sqrt{x-3}$, which of the following describes the domain?

Accepted Answer

$x \geq 3$

Question 12

A function $h(x)$ is defined as $h(x) = \dfrac{x^2 - 1}{x - 1}$ for $x 
eq 1$. What is $h(2)$?

Accepted Answer

$3$

Question 13

Given $f(x) = x^2$ and $g(x) = x^2$ for $x \geq 0$, are $f$ and $g$ equal?

Accepted Answer

No, because their domains are different.

Question 14

A chemical reaction rate is modeled by $r(x) = \dfrac{x}{x^2 - 4}$. What values of $x$ are excluded from the domain?

Accepted Answer

$x = 2$ and $x = -2$

Question 15

If $f(x) = x^2$ and $g(x) = x^2$ for $x \leq 1$, which of the following is true?

Accepted Answer

They are equal only for $x \leq 1$.

Question 16

Find the value of the difference quotient $\dfrac{f(x+h) - f(x)}{h}$ for $f(x) = 3x + 5$.

Accepted Answer

$3$

Question 17

A function $f$ is defined by $f(x) = \dfrac{1}{x-3}$. What is the domain of $f$?

Accepted Answer

$x 
eq 3$

Question 18

If $f(x) = x^2$ and $g(x) = x^2$ for $x 
eq 1$, are $f$ and $g$ equal?

Accepted Answer

No, because their domains are different.

Question 19

A function $f$ is defined as $f(x) = \dfrac{x^2 - 4}{x - 2}$ for $x 
eq 2$. What is $f(3)$?

Accepted Answer

$5$

Functions: Definitions, Domains, and Difference Quotients in Precalculus

Study Guide - Practice Questions