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

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-3leq xleq - 2$?

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-3leq xleq - 2$?

Answer

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 (\frac{f(b)-f(a)}{b - a}). Here, (a=-3) and (b = - 2).

Step2: Find (f(-3)) and (f(-2)) from the graph

From the graph, when (x=-3), (y = f(-3)=12) (since the point ((-3,12)) is on the graph). When (x=-2), (y=f(-2)=2) (since the point ((-2,2)) is on the graph).

Step3: Substitute into the formula

Substitute (a=-3), (b=-2), (f(a) = 12), and (f(b)=2) into the formula (\frac{f(b)-f(a)}{b - a}). We get (\frac{2-12}{-2-(-3)}). First, simplify the numerator: (2 - 12=-10). Then simplify the denominator: (-2-(-3)=-2 + 3=1). So (\frac{-10}{1}=-10).

Answer:

(-10)