Chapter 3.7, Problem 25E

To determine

To write: an equation that represents the transformation: vertical shrink by a factor of $\frac{1}{4}$ of the graph of $g\left(x\right)=\left|x\right|$ .

Answer to Problem 25E

  $f\left(x\right)=\frac{1}{4}\left|x\right|$

Explanation of Solution

Concept used:

Vertical transformation:

Relative to the graph of $f\left(x\right)$ , the transformation of graph of $g\left(x\right)=cf\left(x\right)$ is a vertical shrink by a factor of $c$ when $0<c<1$ and is a vertical stretch by a factor of $c$ when $c>1$ .

The required function is the vertical shrink by a factor of $\frac{1}{4}$ of the graph of $g\left(x\right)=\left|x\right|$ .

Since, it is the vertical transformation then by the above definition, the function is of the form $f\left(x\right)=cg\left(x\right)$ .

Also, it is known that it is a vertical shrink by a factor of $\frac{1}{4}$ , it gives that $c=\frac{1}{4}$ .

Thus, the required equation is:

  $\begin{array}{c}f\left(x\right)=cg\left(x\right)\\ =\frac{1}{4}\left|x\right|\end{array}$