Every rational function has a story told by its asymptotes. This guide covers the three types — vertical, horizontal, and slant — and shows when each appears. Vertical asymptotes come from the denominator's zeros (after cancelling common factors with the numerator). Horizontal asymptotes follow the degree-comparison rule: top smaller → y = 0, equal → ratio of leading coefficients, top bigger → none. Slant asymptotes appear when the numerator's degree is exactly one higher than the denominator's; find them with polynomial long division. The guide also distinguishes holes from vertical asymptotes (the cancelling-factor case), shows how limits at infinity ground the algebraic rules in Calc 1, and walks through worked examples for Algebra 2, AP Precalculus, and intro Calc.