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 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 = 1).

Step2: Find (f(-1)) and (f(1)) from the graph

From the graph, when (x=-1), (f(-1)=-20) (since the point ((-1,-20)) lies on the graph of (y = f(x))), and when (x = 1), (f(1)=40) (since the point ((1,40)) lies on the graph of (y = f(x))).

Step3: Substitute values into the formula

Substitute (a=-1), (b = 1), (f(a)=-20), and (f(b)=40) into the formula (\frac{f(b)-f(a)}{b - a}). We get (\frac{40-(-20)}{1-(-1)}=\frac{40 + 20}{1 + 1}).

Step4: Simplify the expression

(\frac{60}{2}=30).

Answer:

(30)