Question

the graph of a function g is shown below.
use the graph of the function to find its average rate of change from x = 0 to x = 3.
simplify your answer as much as possible.

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = g(x)\) from \(x=a\) to \(x = b\) is given by \(\frac{g(b)-g(a)}{b - a}\). Here, \(a = 0\) and \(b=3\).

Step2: Determine \(g(0)\) and \(g(3)\) from the graph

From the graph, when \(x = 0\), \(g(0)=4\); when \(x = 3\), \(g(3)=10\).

Step3: Substitute values into the formula

Substitute \(a = 0\), \(b = 3\), \(g(0)=4\), and \(g(3)=10\) into \(\frac{g(b)-g(a)}{b - a}\). We get \(\frac{10 - 4}{3-0}\).

Step4: Simplify the expression

\(\frac{10 - 4}{3-0}=\frac{6}{3}=2\).

Answer:

\(2\)