Chapter 1.1, Problem 22E

To determine

To graph: The given function and its parent function and then to describe the transformation.

Answer to Problem 22E

The graph of $h(x)=\frac{1}{3}{x}^2$ is a vertical compression by a factor of $\frac{1}{3}$ with respect to the graph of the parent quadratic function.

Explanation of Solution

Given information: Given function is $h(x)=\frac{1}{3}{x}^2$ .

Graph:

The function $h$ is a quadratic function. Using a table of values to graph the given function and the parent function $g(x)=x^2$ ,

  $\begin{array}{lll}x\hfill & g(x)=x^2\hfill & h(x)=\frac{1}{3}{x}^2\hfill \\ -2\hfill & 4\hfill & \frac{4}{3}\hfill \\ -1\hfill & 1\hfill & \frac{1}{3}\hfill \\ 0\hfill & 0\hfill & 0\hfill \\ 1\hfill & 1\hfill & \frac{1}{3}\hfill \\ 2\hfill & 4\hfill & \frac{4}{3}\hfill \end{array}$

So, the required graph is:

  

Interpretation:

The graph of $h$ (shown by blue colored line) is a vertical compression by a factor of $\frac{1}{3}$ w.r.t. the graph of the parent quadratic function $g(x)=x^2$ (shown by green colored line).

So, the graph of $h(x)=\frac{1}{3}{x}^2$ is a vertical compression by a factor of $\frac{1}{3}$ with respect to the graph of the parent quadratic function.