Multivariable Functions & Domain

So how do we find the domain of multivariable functions??

Instead of graphing a curve on a plane like we are used to, multivariable functions of 2 variables graph surfaces in space! Any more than 2 independent variables, and it is really difficult to visualize.

Multivariable Functions

A multivariable function is, simply, a function with more than one variable.

To find the domain of a function of more than one variable, we follow the same procedure that we used in Calculus I on functions of only one variable...We exclude inputs that lead to complex numbers or division by zero.

Basically, the total number of variables represents the number of dimensions in which the graph exists.We are used to 2-D graphs in 2 variables, usually x and y.

See two examples of finding and sketching the domain below!