select all the intervals where h is decreasing. choose all answers that apply: -4 < x < -3 -2 < x < 0 0 < x…

select all the intervals where h is decreasing. choose all answers that apply: -4 < x < -3 -2 < x < 0 0 < x < 2 none of the above

select all the intervals where h is decreasing. choose all answers that apply: -4 < x < -3 -2 < x < 0 0 < x < 2 none of the above

Answer

Answer:

A. $-4 < x < -3$

Explanation:

Step1: Recall decreasing - function property

A function $y = h(x)$ is decreasing on an interval if for any two points $x_1$ and $x_2$ in the interval with $x_1<x_2$, we have $h(x_1)>h(x_2)$. Graphically, the function is decreasing when the graph is going down - hill as we move from left to right.

Step2: Analyze each option

  • For the interval $-4 < x < -3$: Looking at the graph, as $x$ moves from values between $-4$ and $-3$, the $y$ - values of the function $h(x)$ are decreasing.
  • For the interval $-2 < x < 0$: The graph is increasing in this interval since as $x$ increases from values between $-2$ and $0$, the $y$ - values of the function $h(x)$ are increasing.
  • For the interval $0 < x < 2$: The graph is increasing in this interval since as $x$ increases from values between $0$ and $2$, the $y$ - values of the function $h(x)$ are increasing.

So the only interval where $h$ is decreasing is $-4 < x < -3$.