select all the intervals where h is decreasing.\nchoose all answers that apply:\na -5 < x < -4.5\nb 0.5 < x…

select all the intervals where h is decreasing.\nchoose all answers that apply:\na -5 < x < -4.5\nb 0.5 < x < 1\nc 1.5 < x < 2.5\nd none of the above

select all the intervals where h is decreasing.\nchoose all answers that apply:\na -5 < x < -4.5\nb 0.5 < x < 1\nc 1.5 < x < 2.5\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 $-5 < x<-4.5$, the function is decreasing since as $x$ moves from left - to - right (increases), the $y$ - values of the function are going down.
  • In the interval $0.5 < x<1$, the function is increasing as $x$ increases and $y$ also increases.
  • In the interval $1.5 < x<2.5$, the function is decreasing as $x$ increases and $y$ decreases.

Answer:

A. $-5 < x<-4.5$, C. $1.5 < x<2.5$