Piecewise Functions

A courier charges $5 for any package up to 5 pounds, then $2 for each additional pound. The rule for the cost genuinely CHANGES at the 5-pound mark — one formula below, another above. Yet it's a single function, just built from two pieces glued together at a boundary. The world is full of these 'if this, then that' relationships: tax brackets, parking rates, phone plans, speed limits. One function, several rules, each governing its own stretch of the number line.