Chapter 2.1, Problem 17E

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 $g(x)$ .

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

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

  

Graph of $g(x)=-x^2$ Graph of $f(x)=x^2$

Interpretation: Observe the graph carefully; graph of $g(x)=-x^2$ lie below $y-axis$ and graph of $f(x)=x^2$ lie above the $y-axis$ . And nature of graph is parabolic .Because $g(x)=-f(x)$ ,Here $a=-1$ .Hence we can say that $g(x)$ is mirror image of $f(x)$ about $x-axis$ , means Reflection in the $x-axis$ .See the combined graph of $f(x)$ & $g(x)$ .

  

Black graph shows $f(x)=x^2$ and blue graph shows $g(x)=-x^2$ .