Chapter 7.6, Problem 29PPS

To determine

Find the translation of the function.

Answer to Problem 29PPS

The graph of $g\left(x\right)={\left(\frac{2}{7}\right)}^{-6x}$ 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, $g\left(x\right)={\left(\frac{2}{7}\right)}^{-6x}$

Since $g\left(x\right)={\left(\frac{2}{7}\right)}^{-6x}$ so let the parent function be $f\left(x\right)={\left(\frac{2}{7}\right)}^x$

By multiplying $"-6"$ to the exponential part of $f\left(x\right)$ then $g\left(x\right)={\left(\frac{2}{7}\right)}^{-6x}$ 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 $g\left(x\right)={\left(\frac{2}{7}\right)}^{-6x}$ shows reflection with respect to $y-axis$ and bent towards the $y-axis$ .