Periodic Function
A function is periodic if there exists a T>0 such that x(t + T) = x(t).
Therefore the function sin(x) is periodic because there exists a T = 2pi such that sin(t+ 2pi) = sin(t).
Non periodic Function
A example of a non periodic function is a sloped line, like y = 2x + 1. So when the function is shifted by a time T, y(x+T) it is not the same as the function y(x).
