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H(x)=x^2-1. what is the average rate of change of h over the inteval -3

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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 \([-3, a]\).

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