Peace-wise functions

Peace wise functions use more then one equation per graph. We do his to find if the equation is continuous or discontinuous. If there's no holes or gaps or you can draw it with one line, then the functions are continuous. If not then the function are discontinuous. 

The greatest integer function so represented by an x between two double brackets. 

Looks a little something like this. Except for the fact that the lines normally go on and on. This is just a shortened version.  There isn't really a main reason for having these functions, but the main, probably only point is to find whether the graph is continuous or nah.