Question

use the graph below to find the average rate of change of the function from $x = 1$ to $x = 3$.

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) from \(x=a\) to \(x = b\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 1\) and \(b=3\).

Step2: Find \(f(1)\) and \(f(3)\) from the graph

From the graph, when \(x = 1\), \(f(1)=1\); when \(x = 3\), \(f(3)=3\).

Step3: Substitute values into the formula

Substitute \(a = 1\), \(b = 3\), \(f(1)=1\), and \(f(3)=3\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{3 - 1}{3-1}\).

Step4: Simplify the expression

\(\frac{3 - 1}{3-1}=\frac{2}{2}=1\).

Answer:

\(1\)