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 ( 2 leq x leq 8 )?
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 = 2) and (b=8).
Step2: Find (f(2)) and (f(8)) from the graph
From the graph, when (x = 2), (y=f(2)=- 10); when (x = 8), (y = f(8)=-10).
Step3: Substitute into the formula
Substitute (a = 2), (b = 8), (f(2)=-10), and (f(8)=-10) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{-10-(-10)}{8 - 2}=\frac{-10 + 10}{6}).
Step4: Simplify the expression
(\frac{-10 + 10}{6}=\frac{0}{6}=0)
Answer:
(0)