Chapter 1.1, Problem 14E

To determine

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

Answer to Problem 14E

The graph of $f(x)=4+\left|x\right|$ is a vertical translation $4$ units up the graph of the parent absolute value function.

Explanation of Solution

Given information: Given function is $f(x)=4+\left|x\right|$ .

Graph:

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

  $\begin{array}{lll}x\hfill & g(x)=\left|x\right|\hfill & f(x)=4+\left|x\right|\hfill \\ -2\hfill & 2\hfill & 6\hfill \\ -1\hfill & 1\hfill & 5\hfill \\ 0\hfill & 0\hfill & 4\hfill \\ 1\hfill & 1\hfill & 5\hfill \\ 2\hfill & 2\hfill & 6\hfill \end{array}$

So, the required graph is:

  

Interpretation:

The graph of $f$ (shown by blue colored line) is a vertical translation $4$ units up the graph of the parent absolute value function $g(x)=\left|x\right|$ (shown by green colored line).

So, the graph of $f(x)=4+\left|x\right|$ is a vertical translation $4$ units up the graph of the parent absolute value function.