Chapter 7, Problem 60SGR

To determine

To compare: the transformation from $f\left(x\right)=2^x$ to $g\left(x\right)=2^x-3$ and $p\left(x\right)=2^x+4$ .

Explanation of Solution

Given:

The parent function is $f\left(x\right)=2^x$ .

Transformed functions are $g\left(x\right)=2^x-3$ and $p\left(x\right)=2^x+4$ .

Calculation:

For $g\left(x\right)$ ,

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

This decreases the function $f\left(x\right)$ by value 3. The plot of $g\left(x\right)$ will be downward from $f\left(x\right)$ by value 3.

For $p\left(x\right)$ ,

  $\begin{array}{l}p\left(x\right)=2^x+4\left(f\left(x\right)=2^x\right)\\ p\left(x\right)=f\left(x\right)+4\end{array}$

This increases the function $f\left(x\right)$ by value 4. The plot of $g\left(x\right)$ will be upward from $f\left(x\right)$ by value 4.

The plot is shown below: