Chapter 4.7, Problem 56HP

To determine

To write:The absolute value functionof the given graph.

Answer to Problem 56HP

The absolute value function of the given graphis $y=\left|x-6\right|$ .

Explanation of Solution

Given:

The given graph is

  

Calculation:

To write the absolute value function for the graph, observe the given graph. It can be seen that the graph is shifted towards right by the units 6. The upward shift of the graph is zero that means k =0.

From the general function

  $\begin{array}{l}y=a\left|x-h\right|+k\\ a=1\left(\text{Graph is neither compressed nor expanded}\right)\\ k=0\left(\text{The upward shift of the graph is 0}\right)\\ h=6\left(\text{The graph is shifted to right by 6 points}\right)\\ y=1\left|x-6\right|+0\\ y=\left|x-6\right|\end{array}$

Therefore, the function for the graph is $y=\left|x-6\right|$ .