what is the average rate of change from -1 to 1 of the function represented by the graph?

Explanation:

Step1: Recall average - 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, $a=-1$ and $b = 1$.

Step2: Estimate function values from graph

Let's assume that from the graph, when $x=-1$, $y = f(-1)\approx - 0.5$ and when $x = 1$, $y=f(1)\approx - 1.5$.

Step3: Calculate average rate of change

Substitute into the formula: $\frac{f(1)-f(-1)}{1-(-1)}=\frac{-1.5-(-0.5)}{1 + 1}=\frac{-1.5 + 0.5}{2}=\frac{-1}{2}=-0.5$.

Answer:

$-0.5$