Chapter 4.4, Problem 32AYU

To determine

To find:

a. The domain and range of each function.

Answer to Problem 32AYU

a. The domain is $\left\{x|x\ne -1,x\ne 1\right\}$ and range is all real numbers.

Explanation of Solution

Given:

To determine

To find:

b. The intercepts, if any.

Answer to Problem 32AYU

b. The intercepts:

$x\text{-intercept}$: Set $y=0$ then $x=0$, therefore $\left(0,0\right)$.

$y\text{-intercept}$: Set $x=0$ then $y=0$, therefore $\left(0,0\right)$.

Explanation of Solution

Given:

To determine

To find:

c. Horizontal asymptotes, if any.

Answer to Problem 32AYU

c. Horizontal asymptotes: $y=0$.

Explanation of Solution

Given:

To determine

To find:

d. Vertical asymptotes, if any.

Answer to Problem 32AYU

d. Vertical asymptotes $x=-1,x=1$.

Explanation of Solution

Given:

To determine

To find:

e. Oblique asymptotes, if any.

Answer to Problem 32AYU

e. Oblique asymptotes: None.

Explanation of Solution

Given: