use the graph below to find the average rate of change of the function on the interval $1,5$.
use the graph below to find the average rate of change of the function on the interval $1,5$.
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 = 1) and (b=5).
Step2: Find (f(1)) and (f(5)) from the graph
From the graph, when (x = 1), (y=f(1)=1) (since the point ((1,1)) lies on the graph). When (x = 5), (y=f(5)=9) (since the point ((5,9)) lies on the graph).
Step3: Substitute values into the formula
Substitute (a = 1), (b = 5), (f(a)=1), and (f(b)=9) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{9 - 1}{5-1}=\frac{8}{4}).
Answer:
(2)