select all the intervals where f is decreasing.\nchoose all answers that apply:\na -2 < x < -1.5\nb -1 < x <…

select all the intervals where f is decreasing.\nchoose all answers that apply:\na -2 < x < -1.5\nb -1 < x < 0\nc 0 < x < 1\nd none of the above

select all the intervals where f is decreasing.\nchoose all answers that apply:\na -2 < x < -1.5\nb -1 < x < 0\nc 0 < x < 1\nd none of the above

Answer

Answer:

C. (0 < x < 1)

Explanation:

Step1: Recall decreasing - function property

A function (y = f(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 (f(x_1)>f(x_2)).

Step2: Analyze option A

In the interval (- 2<x<-1.5), the function is increasing as the (y) - values are getting larger as (x) increases.

Step3: Analyze option B

In the interval (-1 < x < 0), the function is increasing as the (y) - values are getting larger as (x) increases.

Step4: Analyze option C

In the interval (0 < x < 1), as (x) increases from (0) to (1), the (y) - values of the function (y = f(x)) are getting smaller. So the function is decreasing on the interval (0 < x < 1).

Step5: Analyze option D

Since option C is correct, option D is incorrect.