Question 1

Which of the following best describes the domain of the rational function $$f(x) = \frac{2x+1}{x^2$-4}$$?

Accepted Answer

All real numbers except $$x = 2$$ and $$x = -2$$

Question 2

Given $$f(x) = \frac{x^2$-9}{x-3}$$, what is the x-intercept of the function?

Accepted Answer

The x-intercept is $$x = -3$$

Question 3

For the rational function $$f(x) = \frac{3x^2$+2x+1}{2x^2$-5}$$, what is the horizontal asymptote?

Accepted Answer

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

Question 4

A rational function $$f(x) = \frac{g(x)}{h(x)} is $$written in lowest terms. Which statement is TRUE about its horizontal asymptote?

Accepted Answer

It exists if the degree of $$h(x) is $$greater than or equal to the degree of $$g(x)$$

Question 5

What is the y-intercept of $$f(x) = \frac{4x-8}{x^2$+2x-3}$$?

Accepted Answer

$$y = -\frac{8}{3}$$

Question 6

Which of the following rational functions has a vertical asymptote at $$x = 1$$?

Accepted Answer

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

Question 7

If $$f(x) = \frac{2x^2$+5x+3}{x^2$-4x+4}$$, what is the domain of $$f$$?

Accepted Answer

All real numbers except $$x = 2$$

Question 8

A rational function $$f(x)$$ has a horizontal asymptote at $$y = 0. $$Which of the following could be $$f(x)$$?

Accepted Answer

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

Question 9

Which statement about rational functions is FALSE?

Accepted Answer

A rational function can have more than one horizontal asymptote

Question 10

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

Accepted Answer

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

Question 11

A rational function $$f(x) is $$given by $$f(x) = \frac{5x^3$+2x}{3x^3$-7}. $$What is the horizontal asymptote?

Accepted Answer

$$y = \frac{5}{3}$$

Question 12

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

Accepted Answer

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

Question 13

Which of the following is a step in graphing a rational function?

Accepted Answer

Find the domain and identify vertical asymptotes

Question 14

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

Accepted Answer

$$y = 1$$

Question 15

A rational function $$f(x)$$ has a denominator of degree 3 and a numerator of degree 2. What is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 16

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

Accepted Answer

All real numbers except $$x = -1$$

Question 17

Which of the following is TRUE about the intersection of a rational function with its horizontal asymptote?

Accepted Answer

The graph may intersect its horizontal asymptote

Question 18

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

Accepted Answer

There is no x-intercept

Question 19

If $$f(x) = \frac{2x^2$+3x+1}{x^2$-1}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 1$$ and $$x = -1$$

Rational Functions and Their Graphs: Study Guide

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