Chapter 7.6, Problem 32PPS

To determine

Find the translation of the given function.

Answer to Problem 32PPS

The graph of $g\left(x\right)=2{\left(6.5\right)}^{-x}$ shows reflection with respect to $y-axis$ , show vertical stretch by $factor-2$ .

Explanation of Solution

Given information:

It is given in the question that, $g\left(x\right)=2{\left(6.5\right)}^{-x}$

Since $g\left(x\right)=2{\left(6.5\right)}^{-x}$ so let the parent function be $f\left(x\right)={\left(6.5\right)}^x$

By multiplying $"-1"$ to the exponential part, multiplying by $2$ of $f\left(x\right)$ then $g\left(x\right)=3^{-x}$ 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 with respect to $y-axis$ , when some quantity is multiply to the function which is $">1"$ then the graph show vertical stretch.

So, the graph of $g\left(x\right)=2{\left(6.5\right)}^{-x}$ shows reflection with respect to $y-axis$ , show vertical stretch by $factor-2$ .