Chapter 7.6, Problem 9CYU

To determine

Find the translation of the function of the graph of $f\left(x\right)={\left(\frac{1}{4}\right)}^x$ given function.

Answer to Problem 9CYU

The graph of $g\left(x\right)={\left(\frac{1}{4}\right)}^{-3x}$ shows reflection with respect to $y-axis$ and bent towards the $y-axis$

Explanation of Solution

Given information:

It is given in the question that, $g\left(x\right)={\left(\frac{1}{4}\right)}^{-3x}$

Since $g\left(x\right)={\left(\frac{1}{4}\right)}^{-3x}$ and $f\left(x\right)={\left(\frac{1}{4}\right)}^x$

By multiplying $"-3"$ to the exponential part of $f\left(x\right)$ then $g\left(x\right)={\left(\frac{1}{4}\right)}^{-3x}$ is arrived

So, by the concept of translation of graph when something negative quantity is multiplying in to the exponential part of function then the graph shows reflection and bent towards the $y-axis$ .

So, the graph of $g\left(x\right)={\left(\frac{1}{4}\right)}^{-3x}$ shows reflection with respect to $y-axis$ and bent towards the $y-axis$ .