Question

question 26
use the graph of ( f ) to evaluate the following:
the average rate of change of ( f ) from 1 to ( 3=)
question help: video
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Explanation:

Step1: Recall the formula for average rate of change

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

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

From the graph, when \(x = 1\), \(f(1)=4\); when \(x = 3\), \(f(3)=2\).

Step3: Substitute into the formula

Substitute \(a = 1\), \(b = 3\), \(f(1)=4\), and \(f(3)=2\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{f(3)-f(1)}{3 - 1}=\frac{2 - 4}{3-1}\).

Step4: Simplify the expression

\(\frac{2 - 4}{3 - 1}=\frac{-2}{2}=-1\).

Answer:

\(-1\)