Chapter 7.6, Problem 4BGP

To determine

Find the translation of the graph with respect to the given function $f\left(x\right)=2^x$ .

Answer to Problem 4BGP

The graph of $g\left(x\right)=-1.75{\left(2\right)}^x$ shows reflection with respect to $x-axis$ and the graph show vertical stretch by $factor-1.75$ .

Explanation of Solution

Given information:

It is given in the question that, $g\left(x\right)=-1.75{\left(2\right)}^x$

By multiplying $f\left(x\right)$ to $"-1"$ and $"-1.75"$ then $g\left(x\right)=-1.75{\left(2\right)}^x$ 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 $x-axis$ and when $"-1.75"$ multiply to the function then the graph shows vertical stretch by $factor-1.75$ .

So, the graph of $g\left(x\right)=-1.75{\left(2\right)}^x$ shows reflection with respect to $x-axis$ and the graph show vertical stretch by $factor-1.75$ .