Chapter 4.1, Problem 107AYU

(a)

To determine

Identify the $x-$ intercepts of the graph of $G.$

  $G\left(x\right)={\left(x+3\right)}^2\left(x-2\right)$

Answer to Problem 107AYU

The $x-$ intercepts of the graph of $G$ are $-3,2$ .

Explanation of Solution

Given:

  $G\left(x\right)={\left(x+3\right)}^2\left(x-2\right)$

Calculation:

By given the $G\left(x\right)={\left(x+3\right)}^2\left(x-2\right)$ , $x-$ intercepts of the graph of $G$ is $-3,2$ .

Conclusion:

Hence,the $x-$ intercepts are $-3,2$ .

(b)

To determine

The intercepts of the graph $y=G\left(x+3\right)$ .

  $G\left(x\right)={\left(x+3\right)}^2\left(x-2\right)$

Answer to Problem 107AYU

The $x-$ intercepts of the graph of $G$ are $-6,-1$ .

Explanation of Solution

Given:

Graph: $y=G\left(x+3\right)$

  $G\left(x\right)={\left(x+3\right)}^2\left(x-2\right)$

Calculation:

  $G\left(x+3\right)={\left(x+6\right)}^2\left(x+1\right)$

So,the $x-$ intercepts of the graph of $G$ are $-6,-1$ .

Conclusion:

Hence, the $x-$ intercepts of the graph of $G$ are $-6,-1$ .