Answer:
Explanation:
To find the average rate of change of the function \(h(x) = x^2 - 1\) over the interval \([-3, a]\), where \(a\) is a specific value, you can use the following formula:
\[
\text{Average Rate of Change} = \frac{h(a) - h(-3)}{a - (-3)}
\]
In this case, \(a\) is a variable, so you'll calculate the average rate of change in terms of \(a\):
\[
\text{Average Rate of Change} = \frac{h(a) - h(-3)}{a - (-3)}
\]
Now, plug in the function \(h(x) = x^2 - 1\) and the interval \([-3, a]\):
\[
\text{Average Rate of Change} = \frac{a^2 - 1 - ((-3)^2 - 1)}{a + 3}
\]
Simplify this expression, and you'll have the average rate of change of \(h(x)\) over the interval \([-3, a]\).