Chapter 7, Problem 58SGR

To determine

To describe the transformation g(x) as it relates to the parent function f(x).

Answer to Problem 58SGR

g(x) is the graph of f(x) vertically stretched by a factor of 5.

Explanation of Solution

Given information: Parent function is given below.

  $f(x)=2^x;g(x)=5{(2)}^x.$

Calculation:

A transformation of the form $g(x)=af(x)$ is a vertical stretch when $\left|a\right|>1$ , a vertical compression when $0<\left|a\right|<1$ and a reflection across the x -axis when a <0. If $f(x)=2^x,\text{then}g(x)={5.2}^x=5f(x)\text{so}a=5.$ Since $\left|a\right|>1$ , g(x) is the graph of $f(x)$ vertically stretched by a factor of 5.

So, $$ g(x) is the graph of f(x) vertically stretched by a factor of 5.