select all the intervals where h is decreasing.\nchoose all answers that apply:\na -4 < x < -3\nb -2 < x <…

select all the intervals where h is decreasing.\nchoose all answers that apply:\na -4 < x < -3\nb -2 < x < 0\nc 0 < x < 2\nd none of the above

select all the intervals where h is decreasing.\nchoose all answers that apply:\na -4 < x < -3\nb -2 < x < 0\nc 0 < x < 2\nd none of the above

Answer

Explanation:

Step1: Recall decreasing - function property

A function $y = h(x)$ is decreasing on an interval if as $x$ increases, $y$ decreases. That is, for any two points $x_1$ and $x_2$ in the interval with $x_1<x_2$, we have $h(x_1)>h(x_2)$.

Step2: Analyze the graph

Looking at the graph of $y = h(x)$:

  • In the interval $-4 < x<-3$, as $x$ increases (moves from left - to - right), the $y$ - values of the function are decreasing.
  • In the interval $-2 < x < 0$, as $x$ increases, the $y$ - values of the function are increasing.
  • In the interval $0 < x < 2$, as $x$ increases, the $y$ - values of the function are increasing.

Answer:

A. $-4 < x < -3$