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: $\bigl[\bigl(-\pi, -\frac{\pi}{2}\bigr) \cup \bigl(-\frac{\pi}{2} , 0\bigr)\bigr] + 2\pi k,\quad k \in \mathbb{Z}$