Chapter 2.1, Problem 19E

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 $g(x)$ .

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

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

  

Graph of $g(x)=3x^2$ 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 $g(x)=3x^2$ is expansion of graph on $y-axis$ , If I compare with $g(x)=af(x)$ we will find scaling parameter is $3$ . Which is greater than $1$ , Hence graph will be compressed about $y-axis$ .

  

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