identify the interval(s) on which the function is decreasing.\na. (-3, -2)\nb. (0, -2)\nc. (-∞, -2)\nd. (-∞…

Explanation:

Step1: Recall the definition of a decreasing function

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 each option

• Option A: ((-3,-2)) This is a very small interval. Looking at the graph, we cannot say the function is decreasing over this entire interval.
• Option B: ((0, - 2)) Intervals are written with the smaller number on the left. So ((0,-2)) is an incorrect interval notation.
• Option C: ((-\infty,-2)) If we take two points (x_1<x_2<-2), we cannot be sure from the graph that (f(x_1)>f(x_2)) for all such (x_1) and (x_2) in this interval.
• Option D: ((-\infty,-3)) For any two points (x_1<x_2<-3), from the graph, as (x) increases (moving from left to right) in the interval ((-\infty,-3)), the (y -) values of the function decrease.

Answer:

D. ((-\infty,-3))