Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-2leq xleq -1$?

Explanation:

Step1: Recall 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, \(a=-2\) and \(b = - 1\).

Step2: Find \(f(-2)\) and \(f(-1)\) from the graph

From the graph, when \(x=-2\), \(y=f(-2)=0\); when \(x = - 1\), \(y=f(-1)=20\).

Step3: Substitute values into the formula

Substitute \(a=-2\), \(b=-1\), \(f(a) = 0\), and \(f(b)=20\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{20-0}{-1-(-2)}=\frac{20}{-1 + 2}\).

Step4: Simplify the expression

\(\frac{20}{1}=20\).

Answer:

$20$