In the field of mathematics, a function is a relationship that makes each element in one set correspond to the only element in another (possibly the same) set.

Mathematically, a function is a corresponding relationship from a non-empty number set A to a real number set B. Simply put, A changes with B, and A is a function of B. To be precise, let X be a non-empty number set, Y be a non-empty number set, and F be the corresponding rule. If there is only one element Y corresponding to each X in X according to the corresponding rule F, it is said that the corresponding rule F is a function on X, which is denoted as y=f(x), and X is called the domain of the function F (x), and the set is its range (the range is the corresponding rule, and the domain is two elements of the function).

Functional related concepts

Independent variable, a variable whose function is related to another quantity. Any value in this quantity can find a corresponding fixed value in another quantity.

The dependent variable (function) changes with the change of the independent variable, and only when the independent variable takes a unique value, the dependent variable (function) has and only has a unique value corresponding to it.

Geometric meaning

Functions are related to inequalities and equations (elementary functions). Let the function value be equal to zero, and from the geometric point of view, the corresponding independent variable is the intersection of the image and the X axis; From the algebraic point of view, the corresponding independent variable is the solution of the equation. In addition, replacing "=" in the expression of a function (except a function without expression) with "",and then replacing "y" with other algebraic expressions, the function becomes an inequality, and the value range of the independent variable can be found.