Chapter 9.3, Problem 2ACYP

To determine

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

Answer to Problem 2ACYP

There is an asymptote at $x=3\text{ and }f\left(x\right)=-2$ .

The domain is all real numbers not equal to $3$ and the range is all real numbers not equal to $-2$ .

Explanation of Solution

Given information:

The given graph is:

  

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

  $\begin{array}{l}x-3=0\\ x=3\end{array}$

The function $\text{f}\left(\text{x}\right)$ is undefined for $x=3$ . There is an asymptote at $x=3$ .

From $x=3$ , as the value of $x$ decrease $f\left(x\right)$ values approach $-\text{2}$ and as the value of $x$ increase $f\left(x\right)$ values approach $-2$ . So, there is an asymptote at $\text{f}\left(\text{x}\right)=-2$ .

The domain is all real numbers not equal to $\text{3}$ and the range is all real numbers not equal to $-2$ .