find the average rate of change of g(x) = x³ over the interval -2,1. write your answer as an integer…

Explanation:

Step1: Recall the average - rate - of - change formula

The average rate of change of a function $y = g(x)$ over the interval $[a,b]$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a=-2$, $b = 1$, and $g(x)=x^{3}$.

Step2: Calculate $g(a)$ and $g(b)$

First, find $g(-2)$: $g(-2)=(-2)^{3}=-8$. Then, find $g(1)$: $g(1)=1^{3}=1$.

Step3: Substitute into the formula

Substitute $g(-2)=-8$, $g(1)=1$, $a=-2$, and $b = 1$ into the average - rate - of change formula $\frac{g(b)-g(a)}{b - a}$: $\frac{g(1)-g(-2)}{1-(-2)}=\frac{1-(-8)}{1 + 2}=\frac{1 + 8}{3}=\frac{9}{3}=3$.

Answer:

3