Given the function $g(x)=-x^{2}-9 x+24$, determine the average rate of change of the function over the interval $-9 \leq x \leq-2$.

Step 1 ：Given the function \(g(x)=-x^{2}-9 x+24\), determine the average rate of change of the function over the interval \(-9 \leq x \leq -2\).

Step 2 ：To find the average rate of change of the function over the given interval, we need to calculate the difference in the function values at the endpoints of the interval and divide by the difference in the x-values.

Step 3 ：The average rate of change formula is: \[\frac{g(-2) - g(-9)}{-2 - (-9)}\]

Step 4 ：First, we need to find the values of g(-2) and g(-9).

Step 5 ：\(g(-2) = -(-2)^{2}-9(-2)+24 = 38\)

Step 6 ：\(g(-9) = -(-9)^{2}-9(-9)+24 = 24\)

Step 7 ：Now that we have the values of g(-2) and g(-9), we can plug them into the average rate of change formula and calculate the result.

Step 8 ：\[\frac{g(-2) - g(-9)}{-2 - (-9)} = \frac{38 - 24}{-2 - (-9)} = \frac{14}{7} = 2.0\]

Step 9 ：\(\boxed{\text{The average rate of change of the function over the interval } -9 \leq x \leq -2 \text{ is 2.0}}\)