Chapter 9.3, Problem 1CYU

To determine

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

Answer to Problem 1CYU

There is an asymptote at $x=1\text{ and }f\left(x\right)=0$ .

The domain is all real numbers not equal to $\text{1}$ and the range is all real numbers not equal to $\text{0}$ .

Explanation of Solution

Given information:

The given graph is:

  

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

  $\begin{array}{l}x-1=0\\ x=1\end{array}$

The function $\text{f}\left(\text{x}\right)$ is undefined for $x=1$ . There is an asymptote at $x=1$ .

From $x=1$ , as the value of $x$ decrease $f\left(x\right)$ values approach $\text{0}$ and as the value of $x$ increase $f\left(x\right)$ values approach $\text{0}$ . So, there is an asymptote at $f\left(x\right)=0$ .

The domain is all real numbers not equal to $\text{1}$ and the range is all real numbers not equal to $\text{0}$ .