Limits at Infinity

Push x to a million, a billion, beyond. Most functions don't keep doing anything interesting — they settle toward a single value, a horizontal asymptote. The formal name is a limit at infinity: lim(x→∞) f(x) = L means f(x) gets arbitrarily close to L as x grows without bound. It's the rigorous version of 'end behavior' you met with polynomials, and it explains why a cup of coffee approaches room temperature, why a drug's concentration approaches zero, and why a rational function flattens onto a line. The far edges of a graph have rules of their own.