Chapter 7.6, Problem 6GP

To determine

To compare: The graphs of the given function with the parent function $f\left(x\right)=3^x$ , and then verify using technology.

Explanation of Solution

Given:

The functions $g\left(x\right)=-4\left(3^x\right),p\left(x\right)=0.2{\left(3\right)}^{x+3}-5,q\left(x\right)={\left(3\right)}^{-x}+2$ .

Calculation:

The graph of $g\left(x\right)$ is obtained by reflecting the parent function about x-axis and then stretching in y-direction by a factor of 4.

The graph of $p\left(x\right)$ obtained by shifting the graph of the parent function 3 units to the left, the compressed in y-direction by factor 0.2 followed by a downward shift of 5 units.

The graph of $q\left(x\right)$ is obtained by reflecting the parent function about y-axis followed by an upward shift of 2 units.

Now, graph the given functions and the parent function on the same coordinate plane to verify the result as shown below.