How do I define a piecewise function?

savecancel

Okay, this is actually well documented, though the actual behavior of Piecewise functions leaves a lot to be desired (as the original implementor, David Joyner, would be the first to admit) - nonetheless you can do a fair amount with them, though sometimes not with the same syntax as the rest of Sage.

Try

sage: sage.functions.piecewise??

as well as the documentation for Piecewise and PiecewisePolynomial.