Chapter 3.7, Problem 22E

To determine

To find: the value of a .

Answer to Problem 22E

  $a=\frac{1}{2}$

Explanation of Solution

Given:

The graph:

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 when $0<c<1$ and is a vertical stretch when $c>1$ (where each y value is multiplied by c ).

Comparing the given graphs of $f\left(x\right)=\left|x\right|$ and $w\left(x\right)=a\left|x\right|$ , it can be observed that the graph of w is a vertical shrink of the graph of f by a factor of $\frac{1}{2}$ .

Thus, by the above definition of vertical shrink, it can be said that $a=\frac{1}{2}$ .