Chapter 3.7, Problem 21E

To determine

To find: the value of a .

Answer to Problem 21E

  $a=-3$

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 ).

Reflection in coordinate axes:

The graph of $g\left(x\right)=f\left(-x\right)$ is the reflection in the y -axis of the graph of f.

The graph of $g\left(x\right)=-f\left(x\right)$ is the reflection in the x -axis of the graph of f.

Comparing the given graphs of $f\left(x\right)=\left|x\right|$ and $p\left(x\right)=a\left|x\right|$ , it can be observed that the graph of p is a vertical stretch of the graph of f by a factor of 3 and then a reflection in the x -axis.

Thus, by the above definition of vertical stretch and reflection about x -axis it can be said that $a=-3$ .