Notation when describing properties of a periodic function

Asked Nov 26 '20 at 19:56

Active Nov 26 '20 at 20:17

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When describing intervals of increase, intervals of decrease, and the domain, does it have to be for the same period? For example for the graph of $$y=\sec(x)$$

Is it correct to describe the intervals as such:

Domain: $\bigl[x \in \bigl(-\frac{3\pi}{2}, -\frac{\pi}{2}\bigr) \cup \bigl(-\frac{\pi}{2} , \frac{\pi}{2}\bigr)\bigr] + 2\pi k, \quad k \in \mathbb{Z} $
Interval of increase: $\bigl[\bigl(0, \frac{\pi}{2}\bigr) \cup \bigl( \frac{\pi}{2} , \pi\bigr)\bigr] + 2\pi k,\quad k \in \mathbb{Z}$
Interval of decrease: $\bigl[\bigl(-\pi, -\frac{\pi}{2}\bigr) \cup \bigl(-\frac{\pi}{2} , 0\bigr)\bigr] + 2\pi k,\quad k \in \mathbb{Z}$

edited Nov 26 '20 at 20:17

Bernard

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asked Nov 26 '20 at 19:56

Sinestro 38

As a help, you can compare with the solution that gives WA: increasing f(x)=sec(x). – manooooh Nov 26 '20 at 20:01
Almost correct. For the intervals of , $0$ and $\pi$ belong to the intervals. – Bernard Nov 26 '20 at 20:17
@Bernard What do you mean? I don't think I understand what you're saying. – Sinestro 38 Nov 26 '20 at 21:05
The intervals should be $\bigl[0, \frac{\pi}{2}\bigr) \cup \bigl( \frac{\pi}{2} , \pi\bigr]$ and $\bigl[-\pi, -\frac{\pi}{2}\bigr) \cup \bigl(-\frac{\pi}{2} , 0\bigr]$ respectively. – Bernard Nov 26 '20 at 21:14

Notation when describing properties of a periodic function

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