# Difference between revisions of "Math 22 Functions of Several Variables"

## Definition of a Function of Two Variables

``` Let ${\displaystyle D}$ be a set of ordered pairs of real numbers.
If to each ordered pair ${\displaystyle (x,y)}$ in ${\displaystyle D}$ there corresponds a unique real number ${\displaystyle f(x,y)}$, then ${\displaystyle f}$ is a function of ${\displaystyle x}$ and ${\displaystyle y}$.
The set ${\displaystyle D}$ is the domain of ${\displaystyle f}$, and the corresponding set of values for ${\displaystyle f(x,y)}$ is the range of ${\displaystyle f}$. Functions of three, four, or more variables are defined similarly.
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