determine the average rate of change from x = -1 to x = 1.

Explanation:

Step1: Recall rate - of - change formula

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, $a=-1$, $b = 1$.

Step2: Read function values from graph

From the graph, when $x=-1$, $y = 4$ (i.e., $f(-1)=4$), and when $x = 1$, $y=0$ (i.e., $f(1)=0$).

Step3: Calculate average rate of change

Substitute into the formula: $\frac{f(1)-f(-1)}{1-(-1)}=\frac{0 - 4}{1+1}=\frac{-4}{2}=-2$.

Answer:

$-2$