the graph of a function h is shown below. use the graph of the function to find its average rate of change…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = h(x)$ from $x = a$ to $x = b$ is given by $\frac{h(b)-h(a)}{b - a}$. Here, $a=-7$ and $b = - 5$.

Step2: Read function values from the graph

From the graph, when $x=-7$, assume $h(-7)=8$ (by looking at the $y$ - value of the graph at $x = - 7$), and when $x=-5$, assume $h(-5)=4$ (by looking at the $y$ - value of the graph at $x=-5$).

Step3: Calculate the average rate of change

Substitute $a=-7$, $b = - 5$, $h(-7)=8$ and $h(-5)=4$ into the formula $\frac{h(b)-h(a)}{b - a}$. We get $\frac{h(-5)-h(-7)}{-5-(-7)}=\frac{4 - 8}{-5 + 7}=\frac{-4}{2}=-2$.

Answer:

$-2$