identify the intervals where the graph is increasing and decreasing. if there is mor union (\bigcup) to…

Explanation:

Step1: Recall the definition of increasing and decreasing functions

A function (y = f(x)) is increasing on an interval if for any two points (x_1) and (x_2) in the interval with (x_1<x_2), (f(x_1)<f(x_2)). A function is decreasing on an interval if for any two points (x_1) and (x_2) in the interval with (x_1 < x_2), (f(x_1)>f(x_2)).

Step2: Analyze the graph

• Look at the slope of the tangent line to the graph. When the slope of the tangent line is positive, the function is increasing. When the slope of the tangent line is negative, the function is decreasing.
• For (x\in(-\infty,-3)), as (x) increases, (y) increases. For (x\in(-3, - 1)), as (x) increases, (y) decreases. For (x\in(-1,\infty)), as (x) increases, (y) increases.

Answer:

Increasing on the interval(s) ((-\infty,-3)\cup(-1,\infty)) Decreasing on the interval(s) ((-3,-1))