Chapter 7, Problem 29PT

To determine

To describe: the transformations in $g(x)$ and $p(x)$ related to parent function $f(x)$ .

Explanation of Solution

Given information:

The given functions are as follows.

  $\begin{array}{l}g(x)=-0.15{\left(3\right)}^{x+2}\\ p(x)={\left(3\right)}^{-x}-1\\ f(x)={\left(3\right)}^x\end{array}$

Consider the parent function $f(x)={\left(3\right)}^x$

The graphs of $g(x)$ , $p(x)$ and $f(x)$ are shown below.

  

Hence,

The graph of $g(x)$ is the two units left shift followed by reflection across x- axis followed

by vertical compression by the factor $0.15$ of the function $f(x).$

The graph of $p(x)$ is the one unit right shift followed by reflection across y- axis of the

function $f(x).$