Chapter 9.2, Problem 4BGP

To determine

To graph and describe transformation of the function in relation to the graph of $f(x)=x^2$ .

Explanation of Solution

Given information :

The function that is provided: $g(x)={\left(\frac{2}{5}x\right)}^2$ .

Graph :

Interpretation :

In the graph of quadratic function $f(x)$ when x is multiplied by a positive constant a before the quadratic function $f(x)$ is evaluated, the resultant function $f(ax)$ is horizontally stretched or compressed vertically by a factor of $\frac{1}{\left|a\right|}$ .

If $\left|a\right|$ $>1$ , the graph of $f(x)$ is compressed horizontally, that is, all points on the graph $f(x)$ move closer to the y -axis.

If $\left|a\right|<1$ , the graph of $f(x)$ is stretched horizontally, that is, all points on the graph $f(x)$ move farther away from the y -axis.

In the function $g(x)={\left(\frac{2}{5}x\right)}^2$ , the value of $\left|a\right|<1$ at $a=\frac{2}{5}$ . Thus, the transformation of $f(x)$ when multiplied by a , as seen in the graph, is that it is stretched horizontally by a factor of $\frac{5}{2}$ .