Question

H(x) = x² - 1 Over which interval does h have a negative average rate of change?

Answer 1

Answer: x < 0     Interval Notation: (-∞, 0)

Step-by-step explanation:

This is a parabola. The left side of the parabola has a negative rate of change and the right side of the parabola has a positive rate of change.

So it will have a negative rate of change for all x-values less than the Axis of Symmetry.

h(x) = x² + 0x - 1

     a=1   b=0  c=-1

$AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(0)}{2(1)}\quad =0\qquad \rightarrow \quad x=0$

It has a negative rate of change when x is less than 0