Function is special relation where each input has exactly one output. Notation: f: A → B means f is function from A (domain) to B (codomain). f(x) = y means x maps to y. Definition: If x = a, then f(a) is unique. Domain: all possible inputs; Codomain: all possible outputs; Range: actual outputs f(A). Types: (1) One-one (injective): different inputs → different outputs; (2) Onto (surjective): range = codomain; (3) Bijective: one-one and onto. Example: f: ℝ → ℝ, f(x) = 2x+1. Domain = ℝ, Range = ℝ (bijective). But f: ℕ → ℕ, f(x) = 2x. Range = even naturals (not onto). Solving: Identify domain/codomain/range. Check function properties. Exam tip: Distinguish function from relation. Vertical line test for graphical representation.