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

Explanation:

Step1: Find the function values at endpoints

From the graph, when (x = - 9), (y=f(-9)=-16); when (x=-4), (y = f(-4)=-6).

Step2: Use the average - rate - of - change formula

The formula for 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), (b = - 4), (f(a)=-16), (f(b)=-6). [ \begin{align*} \frac{f(-4)-f(-9)}{-4-(-9)}&=\frac{-6-(-16)}{-4 + 9}\ &=\frac{-6 + 16}{5}\ &=\frac{10}{5} \end{align*} ]

Answer:

(2)