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

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