Definition of a periodic function and its period

A function f is said to be periodic if there is a number p>0 such that f(x+p)=f(x) for all x in the domain of f.

The smallest such number p is called the period of f.

Definition of Amplitude

Let f be a periodic function and let m and M denote the minimum and maximum values of the function, respectively. Then the amplitude of f is the number (M-m)/2.