the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on…
the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -4 leq x leq -2 )?
Answer
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=-4) and (b = - 2).
Step2: Find (f(-4)) and (f(-2)) from the graph
From the graph, when (x=-4), (y = f(-4)=0); when (x=-2), (y=f(-2)=8).
Step3: Substitute into the formula
Substitute (a=-4), (b=-2), (f(a) = 0), and (f(b)=8) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{8 - 0}{-2-(-4)}=\frac{8}{2}=4).
Answer:
(4)