Let d be a set of non-empty ordered arrays of n elements, and f be a corresponding rule. 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.

This is a multivariable function, which can be better understood by combining images.

For pictures, please refer to the Zhihu webpage link.