Chapter 2.1, Problem 3E

To determine

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

Answer to Problem 3E

  

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 $g(x)$ .

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

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

  

Interpretation: Observe the graph carefully; red graph lie above $x-axis$ and blue graph lie above and below, and nature of graph is parabolic. Graph of $g(x)=x^2-3$ is vertical transform of $f(x)=x^2$ . If I compare with $f(x)=x^2+k$ , we found $k=-3$ ,and we can say this transformation is vertical shift-down transformation. Hence we can say that, $g(x)=f(x)-3=x^2-3$ .In above graph red colour graph shows $f(x)=x^2$ .and blue colour graph shows $g(x)=x^2-3$ .