Function y={x}

Recall that {x}=x-[x]., where [x] is the greatest integer that is less or equal than x.

Note, that for any x we have that {x-1}={x}={x+1}.

This means that function y={x} is periodic with period T=1.

If 0<=x<1 then [x]=0. This means that {x}=x-[x]=x-0=x.

Now draw the graph on interval [0,1) and move it parallel n units (n is natural number) right and left along x-axis. As result we obtain graph of the function y={x}.

Graph of the function y={x} is shown. Note, that there are hole points: this means that, for example, near point 1 from left, i.e. at points, 0.8, 0.9, 0.99 etc. [x] equals just x, so the closer x to one, the closer {x} to 1 but at point 1 it is not 1, it is 0. In other words function "jumps down".