quiz 1\ngoogle classroom\nmicrosoft teams\nyou might need: calculator\n$h(x)=x^{2}-1$\nwhat is the average…

quiz 1\ngoogle classroom\nmicrosoft teams\nyou might need: calculator\n$h(x)=x^{2}-1$\nwhat is the average rate of change of ( h ) over the interval ( -3 leq x leq -1 )?\nshow calculator

quiz 1\ngoogle classroom\nmicrosoft teams\nyou might need: calculator\n$h(x)=x^{2}-1$\nwhat is the average rate of change of ( h ) over the interval ( -3 leq x leq -1 )?\nshow calculator

Answer

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)