Question

answer for the following questions about the graph below. answer in interval notation. answer dne if the interval does not exist.
a. in what interval(s) is the function is increasing?
b. in what interval(s) is the function is decreasing?
c. in what interval(s) is the function is constant?

Explanation:

Step1: Analyze the decreasing interval

A function is decreasing when its graph goes down from left to right.
Looking at the given graph, after the point \((\frac{\pi}{2},1)\), the graph goes down as \(x\) increases. Also, before the point \((-\frac{\pi}{2}, - 1)\), the graph goes down as \(x\) decreases.
The function is decreasing on the intervals \((-\infty,-\frac{\pi}{2})\) and \((\frac{\pi}{2},\infty)\)

Answer:

\((-\infty,-\frac{\pi}{2})\cup(\frac{\pi}{2},\infty)\)