Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -9 leq x leq -4 )?

Explanation:

Step1: Find the function values at endpoints

From the graph, when \(x = - 9\), \(y=f(-9)=-16\); when \(x=-4\), \(y = f(-4)=-6\).

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, \(a=-9\), \(b = - 4\), \(f(a)=-16\), \(f(b)=-6\).

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Answer:

\(2\)