What is the period of a periodic function |f(x)| , if period of f(x) is T? If period of the function $f(x)$  is $T$ then what is the period of the function $|f(x)|$.
It can be any divisor of $T$. For example, $T/5$
This is going to depend on whether the function $f(x)$ becomes negative or not and on where those zeroes are (if they exist).
Example 1:
If $f(x)=\sin x + 3$ then both $f(x)$ and $|f(x)|$ have the same period.
Example 2:
If $f(x)=\sin x + 0.5$ then both $f(x)$ and $|f(x)|$ have the same period.
Example 3:
If $f(x)=\sin x$ then $|f(x)|$ has half the period of $f(x)$.
Plot the three different situations and try to see why this is so.