the average rate of change from x = -2 to x = 6 for the function shown in the graph is

Explanation:

Step1: Recall average - rate - of - change formula

The formula for the average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$, $b = 6$, $f(-2)=7$ (from point $B(-2,7)$) and $f(6)=3$ (from point $A(6,3)$).

Step2: Substitute values into the formula

$\frac{f(6)-f(-2)}{6-(-2)}=\frac{3 - 7}{6+2}$.

Step3: Simplify the expression

$\frac{3 - 7}{6 + 2}=\frac{-4}{8}=-\frac{1}{2}$.

Answer:

$-\frac{1}{2}$