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})