Question

what is the average rate of change of g over the interval -1,4? give an exact number.

Explanation:

Step1: Recall the formula for average rate of change

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, \(a=-1\) and \(b = 4\).

Step2: Find \(g(a)\) and \(g(b)\)

From the table, when \(x=-1\), \(g(-1)=5\); when \(x = 4\), \(g(4)=-1\).

Step3: Substitute into the formula

Substitute \(g(-1) = 5\), \(g(4)=-1\), \(a=-1\), and \(b = 4\) into the formula \(\frac{g(b)-g(a)}{b - a}\). We get \(\frac{-1-5}{4-(-1)}=\frac{-6}{5}\).

Answer:

\(-\frac{6}{5}\)