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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