Question

H(x)=x^2−1

Over which interval does h have a negative average rate of change?

Choose 1 answer:

(Choice A)

−3≤x≤5

(Choice B)

1≤x≤4

(Choice C)

−1≤x≤5

(Choice D)

−3≤x≤1

Answer 1

Knowing concepts of polinomial functions and analysis of functions we can find the correct answer to the interval which the average rate of change is negative

(Choice D) : −3≤x≤1

Explicação passo-a-passo:

We have the function H(x)=x^2−1 and we need the interval which the average rate of change is negative.

To calculate this interval we need to use a formula

$R=\frac{f(b)-f(a)}{b-a}$

using the given numbers we can find H(x)

H(1)=0

H(-1)=0

H(-3)=8

H(4)=15

H(5)=24

(Choice A)

$R=\frac{f(5)-f(-3)}{5-(-3)}$

$R=\frac{24-8}{5-(-3)}$

$R=2$

(Choice B)

$R=\frac{f(4)-f(1)}{4-1}$

$R=\frac{15-0}{4-1}$

$R=5$

(Choice C)

$R=\frac{f(5)-f(-1)}{5-(-1)}$

$R=\frac{24-0}{5-(-1)}$

$R=6$

(Choice D)

$R=\frac{f(1)-f(-3)}{1-(-3)}$

$R=\frac{0-8}{1-(-3)}$

$R=-4$