Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-7 leq x leq -2$?

Explanation:

Step1: Identify the formula for average rate of change

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, \(a=-7\) and \(b = - 2\).

Step2: Find \(f(-7)\) and \(f(-2)\) from the graph

From the graph, when \(x=-7\), \(f(-7)=-10\); when \(x = - 2\), \(f(-2)=25\).

Step3: Substitute values into the formula

Substitute \(a=-7\), \(b=-2\), \(f(a)=-10\), and \(f(b)=25\) into \(\frac{f(b)-f(a)}{b - a}\).

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Answer:

\(7\)