Chapter 7.6, Problem 23PPS

To determine

Find the translation of the function.

Answer to Problem 23PPS

The graph of $g\left(x\right)=\frac{1}{3}{\left(\frac{1}{5}\right)}^x$ shows vertical compress by $factor-\frac{1}{3}.$

Explanation of Solution

Given information:

It is given in the question that, $g\left(x\right)=\frac{1}{3}{\left(\frac{1}{5}\right)}^x$

Since, $g\left(x\right)=\frac{1}{3}{\left(\frac{1}{5}\right)}^x$ so let the parent function be $f\left(x\right)={\left(\frac{1}{5}\right)}^x$

By multiplying $f\left(x\right)$ to $"\frac{1}{3}"$ then $g\left(x\right)=\frac{1}{3}{\left(\frac{1}{5}\right)}^x$ is arrived

So, by the concept of translation of graph when some quantity which is $>0and<1$ is multiply to the function then the graph shows vertical compress.

So, the graph of $g\left(x\right)=\frac{1}{3}{\left(\frac{1}{5}\right)}^x$ shows vertical compress by $factor-\frac{1}{3}.$