Piecewise functions

A piecewise function uses one rule on part of the number line and a different rule elsewhere — like a phone plan that charges one rate up to a cap and another beyond it. The interesting action is at the seam where the pieces meet.

At each seam ask the limit question: do the two pieces meet up (continuous) or jump (discontinuous)? Piecewise functions are the natural playground for the one-sided limits you learned earlier.