Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -8 leq x leq -6 )?

Explanation:

Step1: Find the values of \(f(-8)\) and \(f(-6)\)

From the graph, when \(x = - 8\), \(y=f(-8)=-12\); when \(x=-6\), \(y = f(-6)=4\)

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

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, \(a=-8\), \(b = - 6\), \(f(a)=f(-8)=-12\), \(f(b)=f(-6)=4\)

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Answer:

\(8\)