Periodic functions

Concentrate on the function represented in the previous figure. The images of $$\dots ,-4,-2,0,2,4,\dots$$ coincide and they are equal to $0$.

In fact we can observe that the image of any real number $x$ with the images of $$x+2,x+4,\dots$$ We will say that the function is periodic.

A function $f$ is periodic of period $T$ if it exists a positive real number $T$ such that for any $x$ of the domain we have that:$$f(x+T)=f(x)$$Note that if $T$ is a period of the function then also any multiple of $T$ is also a period. The minimum value of $T$ that satisfies the previous definition is known as the fundamental period.