Chapter 7.6, Problem 28PPS

To determine

Find the translation of the given function.

Answer to Problem 28PPS

The graph of $g\left(x\right)=-3{\left(\frac{1}{6}\right)}^x+2$ shows reflection with respect to $x-axis$ the graph show vertical stretch by $factor-3$ and graph shifted $2-unit$ in the positive $y-axis$ .

Explanation of Solution

Given information:

It is given in the question that, $g\left(x\right)=-3{\left(\frac{1}{6}\right)}^x+2$

By multiplying $f\left(x\right)$ to $"-3"$ and adding $"2"$ then $g\left(x\right)=-3{\left(\frac{1}{6}\right)}^x+2$ is arrived

So, by the concept of translation of graph when $"-1"$ is multiplying in the function then the graph shows reflection with respect to $x-axis$ ,when $"3"$ multiply to the function then the graph shows vertical stretch by $factor-3$ and by adding $"2"$ in the exponential part of the function then the graph shifted in the positive $y-axis$

So, the graph of $g\left(x\right)=-3{\left(\frac{1}{6}\right)}^x+2$ shows reflection with respect to $x-axis$ , the graph show vertical stretch by $factor-3$ and graph shifted $2-unit$ in the positive $y-axis$ .