question\nthe function ( y = f(x) ) is graphed below. what is the average rate of change of the function (…

Explanation:

Step1: Recall the average rate of change formula

The average rate of change of a function (y = f(x)) on the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}). Here, (a=-9) and (b = - 8).

Step2: Find (f(-9)) and (f(-8)) from the graph

From the graph, when (x=-9), (y=-40) (so (f(-9)=-40)), and when (x = - 8), (y = 40) (so (f(-8)=40)).

Step3: Substitute into the formula

Substitute (a=-9), (b=-8), (f(a)=-40), and (f(b)=40) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{40-(-40)}{-8-(-9)}=\frac{40 + 40}{-8 + 9}).

Step4: Simplify the expression

(\frac{80}{1}=80).

Answer:

(80)