Function of Two Variables:

Definition: A variable z is called a function of two variables x and y, shown by z = ƒ(x, y), if to every pair of values of x and y (over some domain D), there corresponds a definite value of z.

y and x are known as the Independent variables and z is known as the dependent variable.
   
1. The area A of a rectangle with sides of lengths y and x is A = xy. A is a function of two variables. The domain of the function is x > 0, y > 0.
   
2. The function   is a function of two variables.

The area of this function is {(x, y): x² + y² ≤ 1}.