Question

the function $y = f(x)$ is graphed below. plot a line segment connecting the points on $f$ where $x = -6$ and $x = -2$. use the line segment to determine the average rate of change of the function $f(x)$ on the interval $-6 leq x leq -2$.
plot a line segment by clicking in two locations. click a segment to delete it.

Explanation:

Step1: Find the values of \(f(-6)\) and \(f(-2)\)

From the graph, when \(x = -6\), \(y=f(-6)=-4\); when \(x=-2\), \(y = f(-2)=0\).

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, \(a=-6\), \(b = -2\), \(f(a)=f(-6)=-4\), \(f(b)=f(-2)=0\).

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Answer:

The average rate of change of the function \(f(x)\) on the interval \(-6\leq x\leq-2\) is \(1\).