Question 1

Which of the following is the correct domain for the function $$f(x) = \frac{2x-5}{x-5}$$?

Accepted Answer

$$x 
eq 5$$

Question 2

Given the rational function $$g(x) = \frac{x^2$}{x-5}$$, what is the equation of its vertical asymptote?

Accepted Answer

$$x = 5$$

Question 3

For the function $$h(x) = \frac{x^2$ + 5}{x + 5}$$, which value is excluded from the domain?

Accepted Answer

$$x = -5$$

Question 4

What is the horizontal asymptote of $$f(x) = \frac{2x^2$ + 9}{3x^2$ + 1}$$?

Accepted Answer

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

Question 5

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

Accepted Answer

The graph has no horizontal asymptote.

Question 6

A company’s cost function is $$C(x) = 500{,}000 + 400x. $$What is the average cost function $$\overline{C}(x)$$?

Accepted Answer

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

Question 7

What is the horizontal asymptote of the average cost function $$\overline{C}(x) = \frac{500{,}000}{x} + 400$$?

Accepted Answer

$$y = 400$$

Question 8

If $$f(x) = \frac{x^2$ - 1}{x - 1}$$, what is the simplified form of $$f(x)$$ for $$x 
eq 1$$?

Accepted Answer

$$x + 1$$

Question 9

Which of the following statements about vertical asymptotes is correct?

Accepted Answer

A vertical asymptote occurs where the denominator of a rational function is zero and the numerator is not zero.

Question 10

Given $$f(x) = \frac{2x^2$ + 9}{3x^2$ + 1}$$, what is the $$y-$$intercept of the graph?

Accepted Answer

Question 11

Which arrow notation correctly describes $$x$$ approaching $$a$$ from the left?

Accepted Answer

$$x 	o a^-$$

Question 12

For the rational function $$f(x) = \frac{2x^2$ + 9}{3x^2$ + 1}$$, what is the degree of the numerator and denominator?

Accepted Answer

Numerator: 2, Denominator: 2

Question 13

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

Accepted Answer

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

Question 14

If $$f(x) = \frac{2x^2$ + 9}{3x^2$ + 1}$$, what is the $$x-$$intercept(s) of the graph?

Accepted Answer

There are no real $$x-$$intercepts.

Question 15

Which of the following best describes the meaning of the horizontal asymptote $$y = 400$$ for the average cost function $$\overline{C}(x) = \frac{500{,}000}{x} + 400$$?

Accepted Answer

As production increases, the average cost per wheelchair approaches $400.

Question 16

Which of the following is NOT a step in graphing a rational function?

Accepted Answer

Find the maximum value of the function.

Question 17

If $$f(x) = \frac{2x^2$ + 9}{3x^2$ + 1}$$, what is the behavior of $$f(x) as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o \frac{2}{3}$$

Question 18

Which of the following is the correct interpretation of $$x 	o \infty$$?

Accepted Answer

$$x$$ increases without bound.

Question 19

For the function $$f(x) = \frac{2x^2$ + 9}{3x^2$ + 1}$$, which rule determines the horizontal asymptote?

Accepted Answer

The degrees of numerator and denominator are equal, so the horizontal asymptote is $$y = \frac{2}{3}.$$

Rational Functions and Their Graphs: Study Notes for College Algebra

Study Guide - Practice Questions

Study Guide - Flashcards