Is it piecewise or one equation? is it a mess? Is it a function? If it's a mess, its either piecewise or not a function, depending on if there are any overlaps where there are two values for one x value. If its one line, it's a single line with a single equation. If its more than one line, its piecewise.
Basically if its impossible to define with a single equation, its piecewise. If it is possible, than its just an equation.
As for the equation of the function, I can't help you.
I would show you some examples, but I don't have any.