select all the intervals where h is increasing.\nchoose all answers that apply:\na -4 < x < -3\nb -1 < x <…

select all the intervals where h is increasing.\nchoose all answers that apply:\na -4 < x < -3\nb -1 < x < 0\nc 3.5 < x < 4.5\nd none of the above

select all the intervals where h is increasing.\nchoose all answers that apply:\na -4 < x < -3\nb -1 < x < 0\nc 3.5 < x < 4.5\nd none of the above

Answer

Explanation:

Step1: Recall increasing - function definition

A function $y = h(x)$ is increasing on an interval if as $x$ increases, $y$ also increases. That is, for any two points $x_1$ and $x_2$ in the interval with $x_1<x_2$, we have $h(x_1)<h(x_2)$. Visually, the graph of the function moves up - ward as we move from left to right.

Step2: Analyze option A

For the interval $- 4<x<-3$, as $x$ increases from values close to $-4$ towards $-3$, the $y$ - values of the function $h(x)$ are decreasing. So, the function is not increasing on this interval.

Step3: Analyze option B

For the interval $-1<x<0$, as $x$ increases from values close to $-1$ towards $0$, the $y$ - values of the function $h(x)$ are increasing. The graph of $y = h(x)$ moves upward in this interval.

Step4: Analyze option C

For the interval $3.5<x<4.5$, as $x$ increases from values close to $3.5$ towards $4.5$, the $y$ - values of the function $h(x)$ are decreasing. So, the function is not increasing on this interval.

Answer:

B. $-1 < x < 0$