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 = 4.
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 \(b=4\).

Step2: Find \(g(0)\) and \(g(4)\) from the graph

From the graph, when \(x = 0\), \(g(0)=1\). When \(x = 4\), \(g(4)=16\).

Step3: Substitute values into the formula

Substitute \(g(0)=1\), \(g(4)=16\), \(a = 0\), and \(b = 4\) into \(\frac{g(b)-g(a)}{b - a}\). We get \(\frac{16 - 1}{4-0}=\frac{15}{4}\).

Answer:

\(\frac{15}{4}\)