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 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, $a=-3$, $b = - 1$, and $h(x)=x^{2}-1$.
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: Apply the formula
The average rate of change is $\frac{h(-1)-h(-3)}{-1-(-3)}=\frac{0 - 8}{-1 + 3}=\frac{-8}{2}=-4$.
Answer:
$-4$