Question 1

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

Accepted Answer

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

Question 2

For the function $f(x) = \frac{x+1}{x-2}$, what is the $x$-intercept?

Accepted Answer

$x = -1$

Question 3

Which of the following best describes the domain of $f(x) = \frac{x^2 - 9}{x^2 - 4x + 3}$?

Accepted Answer

All real numbers except $x = 3$ and $x = 1$

Question 4

A rational function $f(x) = \frac{(x-2)(x+1)}{(x-2)(x-3)}$ has a hole at which $x$-value?

Accepted Answer

$x = 2$

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

Question 7

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

Accepted Answer

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

Question 8

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

Question 9

A rational function $f(x) = \frac{x^2 - 9}{x^2 - 4x + 3}$ has which of the following features?

Accepted Answer

Vertical asymptotes at $x = 1$ and $x = 3$

Question 10

Which of the following best describes the horizontal asymptote of $f(x) = \frac{3x^2 + 2}{2x^2 - 5}$?

Accepted Answer

$y = \frac{3}{2}$

Question 11

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

Accepted Answer

$y = x + 1$

Question 12

Which of the following statements is TRUE about the function $f(x) = \frac{x^2 - 4}{x^2 - 1}$?

Accepted Answer

It has vertical asymptotes at $x = 1$ and $x = -1$

Question 13

If the degree of the numerator is exactly one more than the degree of the denominator in a rational function, what type of asymptote does the function have?

Accepted Answer

A slant (oblique) asymptote

Question 14

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

Accepted Answer

$y 	o 1$

Question 15

Which of the following is the correct process to find the $y$-intercept of a rational function $f(x) = \frac{p(x)}{q(x)}$?

Accepted Answer

Evaluate $f(0)$

Question 16

A rational function $f(x) = \frac{x^2 - 4}{x^2 - 1}$ has which of the following horizontal asymptotes?

Accepted Answer

$y = 1$

Question 17

For $f(x) = \frac{x^2 - 1}{x - 1}$, what is the domain?

Accepted Answer

All real numbers except $x = 1$

Question 18

Which of the following is a real-world application of finding vertical asymptotes in rational functions?

Accepted Answer

Determining the time when a chemical reaction rate becomes undefined due to depletion of a reactant

Question 19

If $f(x) = \frac{x^2 - 4}{x^2 - 1}$, which of the following describes the $x$-intercepts?

Accepted Answer

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

Question 20

For $f(x) = \frac{x^2 + 2x + 1}{x + 1}$, what feature does the graph have at $x = -1$?

Accepted Answer

A hole

E4, E5

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