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=-1) and (b = 0).

Step2: Find (f(-1)) and (f(0)) from the graph

From the graph, when (x=-1), (f(-1)=-4) (by looking at the (y) - coordinate of the point on the graph with (x=-1)). When (x = 0), (f(0)=-8) (by looking at the (y) - coordinate of the point on the graph with (x = 0)).

Step3: Substitute into the formula

Substitute (a=-1), (b = 0), (f(a)=-4), and (f(b)=-8) into the formula (\frac{f(b)-f(a)}{b - a}). We get (\frac{-8-(-4)}{0-(-1)}=\frac{-8 + 4}{0 + 1}).

Step4: Simplify the expression

Simplify (\frac{-8 + 4}{0 + 1}). (-8+4=-4) and (0 + 1=1), so (\frac{-4}{1}=-4).

Answer:

(-4)