Question

find the average rate of change from 1 < x < 3

Explanation:

Step1: Determine the function values at endpoints

From the graph, when \(x = 1\), \(y=-2\) (i.e., \(f(1)=-2\)), and when \(x = 3\), \(y = 6\) (i.e., \(f(3)=6\)).

Step2: Use the average - rate - of - change formula

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 1\), \(b=3\), \(f(a)=-2\), \(f(b)=6\).

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Answer:

\(4\)