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 given by (\frac{f(b)-f(a)}{b - a}). Here, (a=-5) and (b = 3).

Step2: Find (f(-5)) and (f(3)) from the graph

From the graph, when (x=-5), (f(-5)=20) (assuming the (y) - value at (x =-5) is (20) as per the grid - like structure of the graph). When (x = 3), (f(3)=-4) (assuming the (y) - value at (x = 3) is (-4) as per the grid - like structure of the graph).

Step3: Substitute into the formula

Substitute (a=-5), (b = 3), (f(a)=20), and (f(b)=-4) into the formula (\frac{f(b)-f(a)}{b - a}). We get (\frac{-4-20}{3-(-5)}=\frac{-24}{8}).

Answer:

(-3)