Question 1

Given the rational function $f(x) = \frac{x^2 - 1}{x^2 - 4}$, which of the following describes its domain?

Accepted Answer

$x 
eq 2,\ x 
eq -2$

Question 2

For the function $f(x) = \frac{x+1}{x^2-9}$, what are the $x$-intercepts?

Accepted Answer

$x = -1$

Question 3

Which of the following best describes the vertical asymptotes of $f(x) = \frac{x+2}{x^2-4}$?

Accepted Answer

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

Question 4

A rational function $f(x) = \frac{x^2-9}{x^2-4x+3}$ has a hole at which $x$-value?

Accepted Answer

$x = 3$

Question 5

Given $f(x) = \frac{2x^2+3}{x^2-1}$, what is the equation of the horizontal asymptote?

Accepted Answer

$y = 2$

Question 6

For $f(x) = \frac{x^2-4}{x-2}$, what is the simplified form and what feature does the graph have?

Accepted Answer

The function simplifies to $x+2$ with a hole at $x=2$

Question 7

Which of the following rational functions has a slant (oblique) asymptote?

Accepted Answer

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

Question 8

If $f(x) = \frac{2x^2+5x+3}{x^2-1}$, what is the $y$-intercept?

Accepted Answer

$(0, 3)$

Question 9

A rational function $f(x) = \frac{x^2-1}{x^2-4}$ is graphed. Which of the following statements is true?

Accepted Answer

There are vertical asymptotes at $x=2$ and $x=-2$

Question 10

For $f(x) = \frac{x^2-4}{x^2+4}$, what is the horizontal asymptote?

Accepted Answer

$y = 1$

Question 11

Which of the following best describes how to find the $x$-intercepts of a rational function $f(x) = \frac{p(x)}{q(x)}$?

Accepted Answer

Set $p(x) = 0$ and solve for $x$

Question 12

Given $f(x) = \frac{x^2-9}{x^2-4x+3}$, what are the vertical asymptotes?

Accepted Answer

$x = 1$ only

Question 13

For $f(x) = \frac{2x^2+3}{x^2-1}$, what is the end behavior as $x 	o \infty$?

Accepted Answer

$f(x) 	o 2$

Question 14

A rational function has a hole at $x = 2$. Which of the following must be true?

Accepted Answer

Both the numerator and denominator have a factor of $(x-2)$

Question 15

For $f(x) = \frac{x^2+2x+1}{x+1}$, what is the equation of the slant asymptote?

Accepted Answer

$y = x+1$

Question 16

Which of the following rational functions has a horizontal asymptote at $y=0$?

Accepted Answer

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

Question 17

If $f(x) = \frac{x^2-4}{x^2-1}$, what are the $x$-intercepts?

Accepted Answer

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

Question 18

For $f(x) = \frac{x^2-1}{x-1}$, what is the simplified form and what feature does the graph have?

Accepted Answer

The function simplifies to $x+1$ with a hole at $x=1$

Question 19

Which of the following best describes the process for finding vertical asymptotes of a rational function?

Accepted Answer

Set the denominator equal to zero and solve for $x$, excluding any common factors with the numerator

Question 20

Given $f(x) = \frac{2x^2+3x+1}{x+1}$, what is the equation of the slant asymptote?

Accepted Answer

$y = 2x+1$

E4-E5

Study Guide - Practice Questions