Chapter 1.1, Problem 30E

To determine

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

Answer to Problem 30E

The graph of $f(x)=\frac{3}{4}\left|x\right|+1$ is a vertical compression by a factor of $\frac{3}{4}$ and vertical translation of $1unit$ upward with respect to the graph of the parent absolute value function.

Explanation of Solution

Given information: Given function is $f(x)=\frac{3}{4}\left|x\right|+1$ .

Graph:

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

  $\begin{array}{lll}x\hfill & g(x)=\left|x\right|\hfill & f(x)=\frac{3}{4}\left|x\right|+1\hfill \\ -2\hfill & 2\hfill & \frac{5}{2}\hfill \\ -1\hfill & 1\hfill & \frac{7}{4}\hfill \\ 0\hfill & 0\hfill & 1\hfill \\ 1\hfill & 1\hfill & \frac{7}{4}\hfill \\ 2\hfill & 2\hfill & \frac{5}{2}\hfill \end{array}$

So, the required graph is:

  

Interpretation:

The graph of $f$ (shown by blue colored line) is a vertical compression by a factor of $\frac{3}{4}$ and vertical translation of $1unit$ upward 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 $f(x)=\frac{3}{4}\left|x\right|+1$ is a vertical compression by a factor of $\frac{3}{4}$ and vertical translation of $1unit$ upward with respect to the graph of the parent absolute value function.