Question

what is the average rate of change of g over the interval 0 ≤ x ≤ 9? give an exact number.

Explanation:

Step1: Find the values of \(g(0)\) and \(g(9)\)

From the graph, when \(x = 0\), \(g(0)=-7\). When \(x = 9\), \(g(9)=4\).

Step2: Use the average rate of change formula

The formula for the average rate of change of a function \(y = g(x)\) over the interval \([a,b]\) is \(\frac{g(b)-g(a)}{b - a}\). Here, \(a = 0\), \(b = 9\), \(g(a)=g(0)=-7\), \(g(b)=g(9)=4\).
So, \(\frac{g(9)-g(0)}{9 - 0}=\frac{4-(-7)}{9}=\frac{4 + 7}{9}\).

Answer:

\(\frac{11}{9}\)