Chapter 2.1, Problem 20E

To determine

To draw: The graph of functions, and describe the transformation of $f(x)$ .

Explanation of Solution

Given information: In the question, two quadratic functions $f(x)$ and $g(x)$ is given. We will draw the graph of each function, and see the transformation of function $f(x)$ to find $g(x)$ .

  $\begin{array}{l}f(x)=x^2\\ g(x)=\frac{x^2}{3}\end{array}$

Graph: In graph gap between two vertical lines and two horizontal lines is 1unit.

  

Graph of $g(x)=\frac{x^2}{3}$ Graph of $f(x)=x^2$

Interpretation: Observe the graph carefully; both graph lie above $y-axis$ .and nature of graph is parabolic. Graph of $g(x)=\frac{x^2}{3}$ is expansion of graph on $y-axis$ , If I compare with $g(x)=af(x)$ we will find scaling parameter is $a=\frac{1}{3}$ which is less than $1$ . Hence graph will be expanded about $y-axis$ .

  

See the above graph, Red graph shows $g(x)=\frac{x^2}{3}$ and blue graph shows $f(x)=x^2$ .