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, $a=-6$ and $b = - 4$.

Step2: Read function values from the graph

From the graph, when $x=-6$, $h(-6)=0$; when $x=-4$, $h(-4)=4$.

Step3: Calculate the average rate of change

Substitute $h(-6)=0$, $h(-4)=4$, $a=-6$, and $b = - 4$ into the formula: $\frac{h(-4)-h(-6)}{-4-(-6)}=\frac{4 - 0}{-4 + 6}=\frac{4}{2}=2$.

Answer:

$2$