Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-6leq xleq -2$?

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, \(a=-6\) and \(b = - 2\).

Step2: Find \(f(-6)\) and \(f(-2)\) from the graph

From the graph, when \(x=-6\), \(f(-6)=-5\) (the \(y\) - coordinate of the point on the graph with \(x = - 6\)). When \(x=-2\), \(f(-2)=15\) (the \(y\) - coordinate of the point on the graph with \(x=-2\)).

Step3: Substitute values into the formula

Substitute \(a=-6\), \(b=-2\), \(f(a)=-5\), and \(f(b)=15\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{15-(-5)}{-2-(-6)}=\frac{15 + 5}{-2 + 6}=\frac{20}{4}\).

Answer:

\(5\)