Types of functions: (1) Constant: f(x) = c for all x; (2) Linear: f(x) = ax + b; (3) Quadratic: f(x) = ax² + bx + c; (4) Polynomial: sum of power terms; (5) Rational: ratio of polynomials; (6) Even: f(-x) = f(x); (7) Odd: f(-x) = -f(x); (8) Periodic: f(x+p) = f(x); (9) Inverse: f⁻¹ exists if f is bijective. Even function examples: f(x) = x², cos(x), |x|. Odd function examples: f(x) = x, sin(x), x³. Solving: Identify function type from equation. Check symmetry for even/odd. Find inverse for bijective functions. Exam tip: Even functions symmetric about y-axis; odd about origin. Inverse function: swap x and y, solve. Practice: Composite functions f(g(x)).