A bivariate function is a mathematical function that involves two independent variables. It can be expressed in the form f(x, y) , where x and y are the inputs. The output of the function depends on the values of both variables, allowing for a wide range of relationships and behaviors. Bivariate functions are often represented graphically in three-dimensional space, where the x-axis and y-axis correspond to the independent variables, and the z-axis represents the output. These functions are commonly used in various fields, including economics, physics, and statistics, to model relationships between two quantities. For example, in economics, a bivariate function might represent the relationship between supply and demand. Understanding bivariate functions is essential for analyzing how changes in one variable can affect another, providing valuable insights in both theoretical and practical applications.