Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( 0 leq x leq 5 )?

Explanation:

Step1: Recall the average rate of change formula

The average rate of change of a function \(y = f(x)\) on the interval \([a,b]\) is given by \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 0\) and \(b=5\).

Step2: Determine \(f(0)\) and \(f(5)\) from the graph

From the graph, when \(x = 0\), \(y=f(0)=0\); when \(x = 5\), \(y = f(5)=40\).

Step3: Calculate the average rate of change

Substitute \(a = 0\), \(b = 5\), \(f(0)=0\), and \(f(5)=40\) into the formula \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{40-0}{5 - 0}=\frac{40}{5}=8\).

Answer:

\(8\)