Chapter 1.1, Problem 26E

To determine

To graph: The given function and its parent function and then to describe the transformation.

Answer to Problem 26E

The graph of $f(x)=\frac{1}{2}\left|x\right|$ is a vertical compression by a factor of $\frac{1}{2}$ , with respect to the graph of the parent absolute value function.

Explanation of Solution

Given information: Given function is $f(x)=\frac{1}{2}\left|x\right|$ .

Graph:

The function $f$ is a absolute value function. Using a table of values to graph the given function and the parent function $g(x)=\left|x\right|$ ,

  $\begin{array}{lll}x\hfill & g(x)=\left|x\right|\hfill & f(x)=\frac{1}{2}\left|x\right|\hfill \\ -2\hfill & 2\hfill & 1\hfill \\ -1\hfill & 1\hfill & \frac{1}{2}\hfill \\ 0\hfill & 0\hfill & 0\hfill \\ 1\hfill & 1\hfill & \frac{1}{2}\hfill \\ 2\hfill & 2\hfill & 1\hfill \end{array}$

So, the required graph is:

  

Interpretation:

The graph of $f$ (shown by blue colored line) is a vertical compression by a factor of $\frac{1}{2}$ w.r.t. the graph of the parent absolute value function $g(x)=\left|x\right|$ (shown by green colored line).

So, the graph of $f(x)=\frac{1}{2}\left|x\right|$ is a vertical compression by a factor of $\frac{1}{2}$ , with respect to the graph of the parent absolute value function.