Q: Simplify $f(x) = \frac{x^2-1}{x-1}$ and state its domain.

$f(x) = x+1$, domain: $x \neq 1$

Q: Write $f(x) = \frac{x^2-4}{x^2+2x-8}$ in lowest terms and state its domain.

$f(x) = \frac{x+2}{x+4}$, domain: $x \neq 2, x \neq -4$

Q: Given $f(x) = \frac{2x^2-8}{x^2-4}$, write $f(x)$ in lowest terms and state the domain.

$f(x) = 2$, domain: $x \neq 2, x \neq -2$

Q: If $f(x) = \frac{5x-10}{x^2-4}$, what is $f(x)$ in lowest terms?

$\frac{5}{x+2}$, \quad x \neq 2, x \neq -2$

Question 1

Which of the following best describes a rational function?

Accepted Answer

A function with a polynomial in the numerator and denominator.

Question 2

Given $f(x) = \frac{12}{x-1}$, what is the domain of $f(x)$?

Accepted Answer

$x 
eq 1$

Question 3

Which value of $x$ makes the denominator of $f(x) = \frac{1}{x^2-1}$ equal to zero?

Accepted Answer

$x = 1$ or $x = -1$

Question 4

Simplify $f(x) = \frac{x^2-1}{x-1}$ and state its domain.

Accepted Answer

$f(x) = x+1$, domain: $x 
eq 1$

Question 5

Which of the following is NOT a rational function?

Accepted Answer

$f(x) = \sqrt{x}$

Question 6

Find the domain of $f(x) = \frac{2x}{x^2-4}$.

Accepted Answer

$x 
eq 2, x 
eq -2$

Question 7

Write $f(x) = \frac{x^2-4}{x^2+2x-8}$ in lowest terms and state its domain.

Accepted Answer

$f(x) = \frac{x+2}{x+4}$, domain: $x 
eq 2, x 
eq -4$

Question 8

If $f(x) = \frac{3x+2}{x-5}$, which value is excluded from the domain?

Accepted Answer

$x = 5$

Question 9

A rational function models the concentration $C(t) = \frac{100}{t-2}$ of a chemical in a solution, where $t$ is time in hours. When is the concentration undefined?

Accepted Answer

At $t = 2$ hours

Question 10

Which of the following rational functions has a domain of all real numbers except $x = -3$ and $x = 2$?

Accepted Answer

$f(x) = \frac{x+1}{x^2+x-6}$

Question 11

Given $f(x) = \frac{2x^2-8}{x^2-4}$, write $f(x)$ in lowest terms and state the domain.

Accepted Answer

$f(x) = 2$, domain: $x 
eq 2, x 
eq -2$

Question 12

Which step is necessary when simplifying a rational function?

Accepted Answer

Factor numerator and denominator, then cancel common factors.

Question 13

If $f(x) = \frac{5x-10}{x^2-4}$, what is $f(x)$ in lowest terms?

Accepted Answer

$\frac{5}{x+2}$, \quad x 
eq 2, x 
eq -2$

Question 14

A rational function $f(x)$ has a denominator $x^2+2x-8$. Which values must be excluded from the domain?

Accepted Answer

$x = -4, x = 2$

Question 15

Which of the following is the correct process to find the domain of a rational function?

Accepted Answer

Set the denominator equal to zero and solve for $x$.

Introduction to Rational Functions: Definitions, Domains, and Simplification

Study Guide - Practice Questions

Study Guide - Flashcards