Question 1

Which of the following best describes the domain of the rational function $$f(x) = \frac{2x+1}{x^2$-9}$$?

Accepted Answer

All real numbers except $$x = 3$$ and $$x = -3$$

Question 2

Given the rational function $$g(x) = \frac{x^2$+4}{x-2}$$, what is the equation of its vertical asymptote?

Accepted Answer

$$x = 2$$

Question 3

For the function $$h(x) = \frac{3x^2$ - 5}{x^2$ + 1}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 3$$

Question 4

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

Accepted Answer

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

Question 5

A rational function $$R(x)$$ has a denominator with a zero at $$x = 4 of $$multiplicity 2. What does the graph do near $$x = 4$$?

Accepted Answer

The graph approaches $$+\infty or$$ $$-\infty on $$both sides of $$x = 4$$

Question 6

Suppose $$f(x) = \frac{5x^4$ - 2x^2$ + 1}{x^2$ + 3}. $$What is the end behavior of $$f(x) as$$ $$x 	o \infty$$?

Accepted Answer

The graph behaves like $$y = 5x^2$

Question 7

Which of the following statements is TRUE about the graph of $$y = \frac{1}{x^2$}$$?

Accepted Answer

It has a vertical asymptote at $$x = 0$$ and a horizontal asymptote at $$y = 0$$

Question 8

A rational function $$f(x)$$ has a numerator of degree 3 and a denominator of degree 2. What type of asymptote does it have?

Accepted Answer

An oblique (slant) asymptote

Question 9

If $$f(x) = \frac{x^2$ - 1}{x^2$ - 4}$$, what are the equations of the vertical asymptotes?

Accepted Answer

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

Question 10

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

Accepted Answer

$$y = \frac{7}{2}$$

Question 11

A chemical reaction rate is modeled by $$R(t) = \frac{10}{t^2$ + 1}. $$What happens to the reaction rate as time $$t$$ increases without bound?

Accepted Answer

It approaches zero

Question 12

Which of the following rational functions has a hole in its graph?

Accepted Answer

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

Question 13

If the denominator of a rational function has a zero of odd multiplicity, what is the behavior of the graph near the corresponding vertical asymptote?

Accepted Answer

The graph approaches $$+\infty on $$one side and $$-\infty on $$the other side

Question 14

Given $$f(x) = \frac{2x^2$ + 3x + 1}{x^2$ - 4x + 4}$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = 2$$

Question 15

Which of the following best describes the end behavior of $$f(x) = \frac{4x^5$ + 1}{x^3$ - 2} as$$ $$x 	o \infty$$?

Accepted Answer

The graph behaves like $$y = 4x^2$

Question 16

A rational function $$f(x)$$ has a numerator of degree 2 and a denominator of degree 4. What is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Study Guide: Properties of Rational Functions (Precalculus Chapter 3.5)

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