Question

question
the function ( y = f ( x ) ) is graphed below. what is the average rate of change of the function ( f ( x ) ) on the interval ( 1 leq x leq 3 )?
answer attempt 2 out of 2

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, \(a = 1\) and \(b=3\).

Step2: Determine \(f(1)\) and \(f(3)\) from the graph

From the graph, when \(x = 1\), \(y=f(1)=8\); when \(x = 3\), \(y = f(3)=-4\).

Step3: Substitute values into the formula

Substitute \(a = 1\), \(b = 3\), \(f(1)=8\), and \(f(3)=-4\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{-4 - 8}{3-1}=\frac{-12}{2}\).

Answer:

\(-6\)