Question 1

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

Accepted Answer

$$(-\infty, 4) \cup (4, \infty)$$

Question 2

Given the rational function $$g(x) = \frac{x^2$ - 25}{x^2$ - 9}$$, which values must be excluded from the domain?

Accepted Answer

$$x = 3$$ and $$x = -3$$

Question 3

Which of the following statements best describes a vertical asymptote of a rational function?

Accepted Answer

A line $$x = a$$ where the function increases or decreases without bound as $$x$$ approaches $$a$$

Question 4

Find the vertical asymptotes of $$f(x) = \frac{x+2}{x^2$-4}.$$

Accepted Answer

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

Question 5

Which of the following rational functions has no vertical asymptotes?

Accepted Answer

$$h(x) = \frac{x^2$ + 1}{x^2$ + 4}$$

Question 6

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

Accepted Answer

$$y = 5$$

Question 7

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

Accepted Answer

$$y = 0$$

Question 8

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

Accepted Answer

$$f(x) = \frac{2x^2$ + 3}{x+1}$$

Question 9

A company has a fixed monthly cost of $$500,000 and a variable cost of 400$ per wheelchair produced. What is the average cost function $$\overline{C}(x)$$ for producing x$ wheelchairs?

Accepted Answer

$$\overline{C}(x) = \frac{500,000}{x} + 400$$

Question 10

For the average cost function $$\overline{C}(x) = \frac{500,000}{x} + 400$$, what does the horizontal asymptote represent in the context of wheelchair production?

Accepted Answer

The minimum possible average cost per wheelchair as production increases

Question 11

Which transformation shifts the graph of $$f(x) = \frac{1}{x}$$ two units to the left and one unit down?

Accepted Answer

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

Question 12

If $$f(x) = \frac{3x-6}{x-2}$$, what is the equation of the slant asymptote?

Accepted Answer

$$y = 3$$

Question 13

Which of the following best describes the end behavior of $$f(x) = \frac{2x^3$ + 1}{x^2$ + 1} as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x)$$ increases without bound (no horizontal asymptote)

Question 14

Which of the following rational functions is even?

Accepted Answer

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

Question 15

Suppose $$f(x) = \frac{x^2$ - 4}{x^2$ - 1}. $$What are the $$x-$$intercepts of the graph?

Accepted Answer

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

Question 16

A rational function $$f(x)$$ has a vertical asymptote at $$x = 3$$ and a horizontal asymptote at $$y = 0. $$Which of the following could be $$f(x)$$?

Accepted Answer

$$f(x) = \frac{2}{x-3}$$

Question 17

If $$f(x) = \frac{4x^2$ + 1}{2x^2$ + 3}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 2$$

Question 18

Which of the following best describes the symmetry of $$f(x) = \frac{1}{x}$$?

Accepted Answer

Origin symmetry (odd function)

Rational Functions and Their Graphs: College Algebra Study Guide

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