# Functions ## Characteristics of Functions - [ ] Vertical line test - [ ] implicit vs explicit functions https://unacademy.com/content/jee/study-material/mathematics/differences-between-implicit-and-explicit-function/ (?) “Certain curves/graphs which are clearly not functions (Ex: failing vertical line test) cannot be explicitly described with a single equation” In general, an equation defines a function implicitly if the function satisfies that equation. An equation may define many different functions implicitly. **Linearity** A function is considered linear if it satisfies two properties: 1. Additivity: $L(u+v) = L(u) + L(v)$ 2. Homogeneity: $L(cu) = cL(u)$ > See also: > - [[Linear Algebra]] ## Special Functions - Polynomial - Exponential - Rational - ![[The Beta Function#^The-Beta-Function]] ![[The Gamma Function#^The-Gamma-Function]] ![[phpDOltYH.png]]