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

Explanation:

Step1: Recall the formula for average rate of change

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: Identify (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 = 20) (so (f(-8)=20)).

Step3: Substitute into the formula

Substitute (a=-9), (b=-8), (f(a)=-40), and (f(b)=20) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{20-(-40)}{-8-(-9)}). Simplify the numerator: (20-(-40)=20 + 40=60). Simplify the denominator: (-8-(-9)=-8 + 9=1). So, (\frac{60}{1}=60).

Answer:

(60)