What if for each ordered array? (x 1, x2, …, xn)∈D, through the corresponding rule f, there is a unique real number y corresponding to it, so the corresponding rule f is called an n-variable function defined on d.

Let it be y=f(x 1, x2, …, xn), where (x 1, x2, …, xn) ∈ D. The variable x 1, x2, …, xn is called the independent variable, and y is called the dependent variable.

When n= 1, it is a univariate function, denoted as y=f(x), x∈D, and when n=2, it is a binary function, denoted as z = f (x, y), (x, y) ∈ d. Functions with two or more variables are collectively called multivariate.

Extended data:

People often say that the function y=f(x) is the relationship between the dependent variable and the independent variable, that is, the value of the dependent variable depends on only one independent variable, which is called a univariate function. But in many practical problems, it is often necessary to study the relationship between the dependent variable and several independent variables, that is, the value of the dependent variable depends on several independent variables.

The essence of multivariate function is a relationship, which is a definite correspondence between two sets. The elements of these two sets can be numbers; It can also be a point, a line, a surface or a body; It also includes vectors, matrices, etc. The result corresponding to one or more elements can be a unique element, that is, a single value. It can also be multiple elements, that is, multiple values.