Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -4 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, \(a=-4\) and \(b = - 2\).

Step2: Find \(f(-4)\) and \(f(-2)\) from the graph

From the graph, when \(x=-4\), \(y = 12\) (so \(f(-4)=12\)), and when \(x=-2\), \(y=-28\) (so \(f(-2)=-28\)).

Step3: Substitute into the formula

Substitute \(a=-4\), \(b=-2\), \(f(a) = 12\), and \(f(b)=-28\) into the formula \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{-28 - 12}{-2-(-4)}=\frac{-40}{2}=-20\).

Answer:

\(-20\)