Chapter 4.7, Problem 32E

To determine

To find: the real zeros of given function, and then describe the transformation of the graph of $f$ that results in the graph of $g$ .

Answer to Problem 32E

From the graph it is very clear that real zeros of $f\left(x\right)$ are $x=-2,x=0$ and $x=2$ .

From the graph it is very clear that real zeros of $g\left(x\right)$ are $x=0,x=2$ and $x=4$ .

The transformation is $g\left(x\right)=f\left(x-2\right)$ .

Explanation of Solution

Given information:

Given graph,

  

Calculation:

From the graph it is very clear that real zeros of $f\left(x\right)$ are $x=-2,x=0$ and $x=2$ .

From the graph it is very clear that real zeros of $g\left(x\right)$ are $x=0,x=2$ and $x=4$

After shifting zeros of $f\left(x\right)$ to the right by 2 units will get the zeros of $g\left(x\right)$ .

  $\begin{array}{c}-2+2=0\\ 0+2=2\\ 2+2=4\end{array}$

Therefore, the transformation is $g\left(x\right)=f\left(x-2\right)$ .