Chapter 2.1, Problem 18E

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; both graph lie above $y-axis$ .and nature of graph is parabolic. Graph of $g(x)={(-x)}^2$ and graph $f(x)=x^2$ are overlap each other because in $g(x)={(-x)}^2$ degree of $-x$ is even. And this will become $x^2$ , Hence there is no effect on graph of $g(x)$ & $f(x)$ .