Answer:
(C)−3 ≤ x ≤ 1
Step-by-step explanation:
The average rate of change of function h over the interval [tex]a \leq x\leq b[/tex], is given by this expression:
[tex]\dfrac{h(b)-h(a)}{b-a}[/tex]
Given the function [tex]h(x)=x^2-1[/tex] on the interval:− 3 ≤ x ≤ 1
[tex]h(1)=1^2-1=0\\h(-3)=(-3)^2-1=9-1=8[/tex]
The average rate of change:
[tex]\dfrac{h(b)-h(a)}{b-a}=\dfrac{0-8}{1-(-3)}=\dfrac{-8}{4}=-2[/tex]
Therefore, the function has a negative average rate of change over the interval − 3 ≤ x ≤ 1.
CHECK:
(A)Average rate of change of h(x) over the interval − 3 ≤ x ≤ 5=2
(B)Average rate of change of h(x) over the interval 1 ≤ x ≤ 4=5
(D)Average rate of change of h(x) over the interval − 1 ≤ x ≤ 5=4
