Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-2leq xleq6$?

Explanation:

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

From the graph, when \(x = - 2\), \(y=f(-2)=20\); when \(x = 6\), \(y = f(6)=-15\).

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, \(a=-2\), \(b = 6\), \(f(a)=f(-2)=20\), \(f(b)=f(6)=-15\).
Substitute into the formula: \(\frac{f(6)-f(-2)}{6-(-2)}=\frac{-15 - 20}{6 + 2}\).

Step3: Calculate the value

\(\frac{-15-20}{6 + 2}=\frac{-35}{8}=-\frac{35}{8}=-4.375\)

Answer:

\(-4.375\)