Rational Functions

Most graphs you've met are continuous — you can draw them without lifting your pencil. A rational function breaks that rule. It's a fraction of two polynomials, P(x)/Q(x), and wherever the denominator Q(x) hits zero, the graph explodes: it rockets toward infinity, or vanishes leaving a tiny hole. These breaks — asymptotes and holes — are the signature of rational functions, and they model every physical situation with a 'can't divide by that' boundary: resistance at zero distance, cost per unit as quantity vanishes.