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 ( 0 leq x leq 9 )?
Answer
Explanation:
Step1: Recall the average rate of change formula
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 = 0) and (b=9).
Step2: Find (f(0)) and (f(9)) from the graph
From the graph, when (x = 0), (y=f(0)=6). When (x = 9), (y=f(9)=-18).
Step3: Substitute into the formula
Substitute (a = 0), (b = 9), (f(0)=6), and (f(9)=-18) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{-18 - 6}{9-0}=\frac{-24}{9}=-\frac{8}{3}).
Answer:
(-\frac{8}{3})