Question

what is the periodic function?

Answer 1

there isn't just one periodic function, there is an infinite number of them.

a periodic function is one that repeats, so
\[f(x) = f(x + n p), n = 1,2,3...\] and \(p\) is the period (length of one complete cycle).

for example \(y = \sin x\) is periodic with \(p = 2\pi\) because \(y = \sin x = \sin( x + 2n\pi)\) for all \(x\) if \(n = 1,2,3...\)