Chapter SH, Problem 9.3.5EP

To determine

The relation between the graph of given function and graph of $f\left(x\right)=x^2.$

Answer to Problem 9.3.5EP

The graph is reflected and stretched vertically.

Explanation of Solution

Given:

The given function is:

  $g\left(x\right)=-3x^2$

Calculation:

Consider the function $g\left(x\right)=-3x^2$ :

As the given function has $-x^2$ , therefore the graph is the reflection of $f\left(x\right)=x^2.$

For this function, the graph is stretched vertically if $\left|a\right|>1$ and is compressed vertically if $0<\left|a\right|<1.$

In the given function,

  $\begin{array}{l}g\left(x\right)=-3x^2\\ a=3\end{array}$

So, the graph is reflected and stretched vertically.

The graph will be: