select all the intervals where g is increasing.\nchoose all answers that apply:\na -4 < x < -3\nb -2.5 < x <…

select all the intervals where g is increasing.\nchoose all answers that apply:\na -4 < x < -3\nb -2.5 < x < -2\nc 0.5 < x < 1.5\nd none of the above

select all the intervals where g is increasing.\nchoose all answers that apply:\na -4 < x < -3\nb -2.5 < x < -2\nc 0.5 < x < 1.5\nd none of the above

Answer

Explanation:

Step1: Recall increasing - function property

A function (y = g(x)) is increasing on an interval if, as (x) increases, (y) also increases. That is, for (x_1<x_2) in the interval, (g(x_1)<g(x_2)). Geometrically, the graph of the function has a positive - slope on the increasing interval.

Step2: Analyze interval (-4 < x < - 3)

Looking at the graph, as (x) moves from values between (-4) and (-3), the (y) - values of the function (g(x)) are decreasing. So the function is not increasing on this interval.

Step3: Analyze interval (-2.5 < x < - 2)

As (x) moves from values between (-2.5) and (-2), the (y) - values of the function (g(x)) are increasing. So the function is increasing on this interval.

Step4: Analyze interval (0.5 < x < 1.5)

As (x) moves from values between (0.5) and (1.5), the (y) - values of the function (g(x)) are increasing. So the function is increasing on this interval.

Answer:

B. (-2.5 < x < - 2), C. (0.5 < x < 1.5)