Chapter 3.7, Problem 23E

To determine

To write: an equation that represents the transformation: vertical translation 7 unit down of the graph of $g\left(x\right)=\left|x\right|$ .

Answer to Problem 23E

  $f\left(x\right)=\left|x\right|-7$

Explanation of Solution

Concept used:

Vertical translation:

The graph of $g\left(x\right)=f\left(x\right)+k$ is a vertical translation of the graph of f .

The vertical shift is k units up if $k>0$ and k units down if $k<0$ .

The required function is the vertical translation 7 unit down of the graph of $g\left(x\right)=\left|x\right|$ .

Since, it is the vertical translation then by the above definition, the function is of the form $f\left(x\right)=g\left(x\right)+k$ .

Also, it is known that translation is 7 units down, it gives that $k=-7$ .

Thus, the required equation is:

  $\begin{array}{c}f\left(x\right)=g\left(x\right)+k\\ =\left|x\right|-7\end{array}$