Question

h(x)=x 2 −1h, left parenthesis, x, right parenthesis, equals, x, squared, minus, 1 Over which interval does h hh have a negative average rate of change? Choose 1 answer: Choose 1 answer: (Choice A) A − 3 ≤ x ≤ 5 −3≤x≤5minus, 3, is less than or equal to, x, is less than or equal to, 5 (Choice B) B 1 ≤ x ≤ 4 1≤x≤41, is less than or equal to, x, is less than or equal to, 4 (Choice C) C − 3 ≤ x ≤ 1 −3≤x≤1minus, 3, is less than or equal to, x, is less than or equal to, 1 (Choice D) D − 1 ≤ x ≤ 5 −1≤x≤5minus, 1, is less than or equal to, x, is less than or equal to, 5 Show Calculator

Answer 1

Answer:

(C)−3 ≤ x ≤ 1

Step-by-step explanation:

The average rate of change of function h over the interval $a \leq x\leq b$, is given by this expression:

$\dfrac{h(b)-h(a)}{b-a}$

Given the function $h(x)=x^2-1$ on the interval:− 3 ≤ x ≤ 1

$h(1)=1^2-1=0\\h(-3)=(-3)^2-1=9-1=8$

The average rate of change:

$\dfrac{h(b)-h(a)}{b-a}=\dfrac{0-8}{1-(-3)}=\dfrac{-8}{4}=-2$

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