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

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

From the graph, when $x=-1$, assume $y = f(-1)=-\frac{1}{2}$ (by estimating the $y$ - value on the graph at $x=-1$). When $x = 1$, assume $y=f(1)=-\frac{3}{2}$ (by estimating the $y$ - value on the graph at $x = 1$).

Step3: Calculate average rate of change

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

Answer:

$-\frac{1}{2}$