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?

Accepted Answer

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?

Accepted Answer

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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