Question 1

Given the function $$f(x) = \frac{2x}{x^2$ - 1}$$, which of the following statements is TRUE about its asymptotes?

Accepted Answer

It has vertical asymptotes at $$x = -1$$ and $$x = 1$$, and a horizontal asymptote at $$y = 0.$$

Question 2

What is the $$y-$$intercept of the function $$f(x) = \frac{2x}{x^2$ - 1}$$?

Accepted Answer

$$y = 0$$

Question 3

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

Accepted Answer

$$f(x) 	o 0$$

Question 4

For the function $$f(x) = \frac{2x}{x^2$ - 1}$$, which value(s) of $$x$$ make the function undefined?

Accepted Answer

$$x = 1$$ and $$x = -1$$

Question 5

What is the $$x-$$intercept(s) of the function $$f(x) = \frac{2x}{x^2$ - 1}$$?

Accepted Answer

$$x = 0$$

Question 6

Which of the following is the correct factorization of the denominator of $$f(x) = \frac{2x}{x^2$ - 1}$$?

Accepted Answer

$$x^2 - 1 = (x + 1)(x - 1$$)$$

Question 7

Suppose $$f(x) = \frac{2x}{x^2$ - 1}$$ models the rate of a chemical reaction, where $$x is $$the concentration of a reactant. What happens to the reaction rate as the concentration increases without bound?

Accepted Answer

The rate approaches zero.

Question 8

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

Accepted Answer

All real numbers except $$x = 1$$ and $$x = -1$$

Question 9

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

Accepted Answer

It is an odd function.

Question 10

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

Accepted Answer

$$f(2) = \frac{4}{3}$$

Question 11

A medical researcher uses $$f(x) = \frac{2x}{x^2$ - 1} to $$model the effect of a drug, where $$x is $$the dosage. For which dosages is the model not valid?

Accepted Answer

For $$x = 1$$ and $$x = -1$$

Question 12

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

Accepted Answer

$$f(x)$$ approaches $$\infty or$$ $$-\infty$$

Question 13

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

Accepted Answer

$$y = 0$$

Question 14

Which of the following is the correct simplified form of $$f(-x)$$ for $$f(x) = \frac{2x}{x^2$ - 1}$$?

Accepted Answer

$$\frac{-2x}{x^2$ - 1}$$

Question 15

Suppose $$f(x) = \frac{2x}{x^2$ - 1}$$ represents the velocity of a particle at time $$x. At $$what time(s) is the particle at rest?

Accepted Answer

At $$x = 0$$

Graphing Rational Functions and Identifying Asymptotes

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