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

Explanation:

Step1: Recall the formula for average rate of change

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 = 1) and (b=3).

Step2: Determine (f(1)) and (f(3)) from the graph

From the graph, when (x = 1), (y=f(1)=8); when (x = 3), (y = f(3)=-4).

Step3: Substitute values into the formula

Substitute (a = 1), (b = 3), (f(1)=8), and (f(3)=-4) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{-4 - 8}{3-1}=\frac{-12}{2}).

Answer:

(-6)