Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -3 leq x leq 3 )?

Explanation:

Step1: Recall the formula for average rate of change

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, \(a=-3\) and \(b = 3\).

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

From the graph, when \(x=-3\), \(f(-3)= - 60\); when \(x = 3\), \(f(3)=50\).

Step3: Calculate the average rate of change

Substitute \(a=-3\), \(b = 3\), \(f(-3)=-60\) and \(f(3)=50\) into the formula \(\frac{f(b)-f(a)}{b - a}\).

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Answer:

\(\frac{55}{3}\)