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}`.graph of the function function y={x}

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".