Chapter 9.3, Problem 2CYU

To determine

To fine the asymptotes, domain and range of each function.

Answer to Problem 2CYU

There is an asymptote at $x=-2\text{ and }f\left(x\right)=1$ .

The domain is all real numbers not equal to $-2$ and the range is all real numbers not equal to $1$ .

Explanation of Solution

Given information:

The given graph is:

  

Find x-values for which $\text{f}\left(\text{x}\right)$ is undefined:

  $\begin{array}{l}x+2=0\\ x=-2\end{array}$

The function $f\left(x\right)$ is undefined for $x=-2$ . There is an asymptote at $x=-2$ .

From $x=-2$ , as the value of $x$ decrease $f\left(x\right)$ values approach $1$ and as the value of $x$ increase $f\left(x\right)$ values approach $1$ . So, there is an asymptote at $f\left(x\right)=1$ .

The domain is all real numbers not equal to $-2$ and the range is all real numbers not equal to $1$ .