what is the average rate of change of g over the interval -1, 2? give an exact number.

Explanation:

Step1: Recall average - rate - of - change formula

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

Step2: Find $g(-1)$ and $g(2)$ from the table

From the table, when $x=-1$, $g(-1)=5$; when $x = 2$, $g(2)=-5$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{g(2)-g(-1)}{2-(-1)}=\frac{-5 - 5}{2 + 1}=\frac{-10}{3}$.

Answer:

$-\frac{10}{3}$