Question

use the graph below to find the average rate of change of the function on the interval $1,5$.

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:

\(2\)