h(x)=x^{2}-1\nwhat is the average rate of change of h over the interval -3≤x≤-1?
h(x)=x^{2}-1\nwhat is the average rate of change of h over the interval -3≤x≤-1?
Answer
Explanation:
Step1: Recall the formula for average rate of change
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))
Substitute (x=-3) into (h(x)=x^{2}-1): (h(-3)=(-3)^{2}-1=9 - 1=8). Substitute (x=-1) into (h(x)=x^{2}-1): (h(-1)=(-1)^{2}-1=1 - 1=0).
Step3: Compute the average rate of change
Using the formula (\frac{h(b)-h(a)}{b - a}), with (h(-1) = 0), (h(-3)=8), (a=-3), and (b=-1), we have (\frac{h(-1)-h(-3)}{-1-(-3)}=\frac{0 - 8}{-1 + 3}=\frac{-8}{2}=-4).
Answer:
(-4)