Definition of function
In mathematics, a function is usually defined as a corresponding relationship that maps an input value (independent variable) to an output value (dependent variable). More formally, a function is a binary relationship in which each input value (independent variable) uniquely corresponds to an output value (dependent variable). The definition of a function usually includes a function name, an input value set (domain) and an output value set (range).
Properties of functions
1, elementary function and transcendental function: Elementary function refers to a function that can be expressed by basic operations (addition, subtraction, multiplication and division, multiplication and division, square root, etc.). ) and constants, such as polynomial function, trigonometric function, exponential function, etc. Transcendental functions refer to functions that cannot be expressed by basic operations and constants, such as logarithmic functions and trigonometric functions.
2. Single-valued function and multi-valued function: A single-valued function refers to a function that has a unique output value (dependent variable) for each input value (independent variable); A multivalued function refers to a function that has multiple output values (dependent variables) for some input values (independent variables).
3. Continuous function and discrete function: continuous function refers to the function defined at every point in its domain; A discrete function is a function that is not defined at a certain point in its domain.
4. Linear function and nonlinear function: linear function refers to the function that satisfies homogeneity and additivity, that is, f (ax+by) = af (x)+BF (y); Nonlinear function refers to a function that does not satisfy homogeneity and additivity.
Representation of function:
1, analytic method: a method of expressing a function with a mathematical formula.
2. Tabular method: a method of listing some independent variables and corresponding dependent variables in a table to represent functions.
3. Image method: a method of representing functions with images.
4. Arrow method: a method of indicating the corresponding relationship between independent variables and dependent variables with arrows.
Function is one of the core concepts of modern mathematics and a mathematical tool to describe the dependence between variables. Functions play an important role in mathematics and computer science.