Question

quiz 1
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microsoft teams
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$h(x)=x^{2}-1$
what is the average rate of change of ( h ) over the interval ( -3 leq x leq -1 )?
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Explanation:

Step1: Recall the average rate of change formula

The average rate of change of a function \(y = h(x)\) over the interval \([a,b]\) is \(\frac{h(b)-h(a)}{b - a}\). Here, \(a=-3\) and \(b = - 1\).

Step2: Calculate \(h(-3)\) and \(h(-1)\)

For \(x=-3\), \(h(-3)=(-3)^{2}-1=9 - 1=8\).
For \(x=-1\), \(h(-1)=(-1)^{2}-1=1 - 1=0\).

Step3: Substitute into the formula

\(\frac{h(-1)-h(-3)}{-1-(-3)}=\frac{0 - 8}{-1 + 3}=\frac{-8}{2}=-4\)

Answer:

\(-4\)