Chapter 2.1, Problem 21E

To determine

To describe: The transformation of function $f(x)=x^2$ to $g(x)={(2x)}^2$ and graph the functions.

Answer to Problem 21E

The function $g(x)={(2x)}^2$ is a horizontal shrink by a factor $\frac{1}{2}$ of the function $f(x)=x^2$ .

  

Explanation of Solution

Given information: Function transformed to $f(x)=x^2$ to $g(x)={(2x)}^2$ .

The function is in the form of $g(x)={(ax)}^2$ , where $a=2$ .

Horizontal shrink occurs when $a>1$ .

From the given function $g(x)={(2x)}^2$ , we know that $a=2$ which is greater than $1$ .

Therefore, we can conclude that the function $g(x)={(2x)}^2$ shrinks horizontally by the factor $\frac{1}{2}$ .