Question 1

Which of the following is the correct domain for the function $$f(x) = \dfrac{x^2$ + 8}{x - 2}$$?

Accepted Answer

$$x 
eq 2$$

Question 2

Given $$f(x) = \dfrac{x^2$ + 6x + 8}{x^2$ - 2x - 8}$$, which values must be excluded from the domain?

Accepted Answer

$$x = 4$$ and $$x = -2$$

Question 3

As $$x$$ approaches $$2$$ from the right in $$f(x) = \dfrac{x^2$ + 8}{x - 2}$$, what happens to $$f(x)$$?

Accepted Answer

$$f(x) 	o +\infty$$

Question 4

Which of the following best describes the behavior of $$\dfrac{1}{x} as$$ $$x$$ approaches $$0$$ from the left?

Accepted Answer

$$\dfrac{1}{x} 	o -\infty$$

Question 5

For $$f(x) = \dfrac{x^2$ - 4}{x^2$ - 4}$$, what is true about its graph?

Accepted Answer

There is a hole at $$x = 2$$ and $$x = -2.$$

Question 6

Given $$f(x) = \dfrac{x^2$ - 25}{x + 5}$$, what are the vertical asymptotes and holes?

Accepted Answer

Hole at $$x = -5$$; no vertical asymptote.

Question 7

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

Accepted Answer

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

Question 8

Find the horizontal asymptote of $$f(x) = \dfrac{3x^2$ + 15}{x^2$ + 1}.$$

Accepted Answer

$$y = 3$$

Question 9

Which of the following best describes the horizontal asymptote of $$f(x) = \dfrac{2x^3$ + 7}{5x^2$ - 2}$$?

Accepted Answer

There is no horizontal asymptote.

Question 10

A chemical reaction's rate is modeled by $$R(t) = \dfrac{4t}{t^2$ + 1}. As $$time $$t$$ increases without bound, what value does $$R(t)$$ approach?

Accepted Answer

$$0$$

Question 11

For $$f(x) = \dfrac{x^2$ - 4x + 4}{x - 2}$$, what is the equation of the slant asymptote?

Accepted Answer

$$y = x - 2$$

Question 12

Which of the following steps is NOT part of the standard process for graphing a rational function $$f(x) = \dfrac{p(x)}{q(x)}$$?

Accepted Answer

Find the minimum value of $$f(x).$$

Question 13

Suppose $$f(x) = \dfrac{x^2$ - 4x + 3}{x^2$ - 9}. $$Which of the following is true about its $$x-$$intercepts?

Accepted Answer

$$x-$$intercepts at $$x = 1$$ and $$x = 3$$

Question 14

A rational function models the concentration of a drug in the bloodstream: $$C(t) = \dfrac{5t}{t^2$ + 4}. $$What is the long-term behavior of $$C(t) as$$ $$t 	o \infty$$?

Accepted Answer

$$C(t) 	o 0$$

Question 15

Given $$f(x) = \dfrac{x^2$ - 1}{x - 1}$$, what is the $$y-$$intercept of the function?

Accepted Answer

$$(0, 1)$$

Question 16

Which of the following rational functions has a hole at $$x = 3$$?

Accepted Answer

$$f(x) = \dfrac{x^2$ - 9}{x - 3}$$

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Suppose $$f(x) = \dfrac{x^2$ - 1}{x - 1}. $$What is the equation of the slant asymptote, if any?

Accepted Answer

$$y = x + 1$$

Question 20

A rational function $$f(x)$$ has a vertical asymptote at $$x = 1$$ and a hole at $$x = -2. $$Which of the following could be $$f(x)$$?

Accepted Answer

$$f(x) = \dfrac{(x + 2)(x - 3)}{(x - 1)(x + 2)}$$

Step-by-Step Guidance: Rational Functions and Their Graphs (College Algebra)

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