Section 14.1: Functions of Several Variables

Definition

A function f of two variables is a rule that assigns to each ordered pair of real numbers \((x, y)\) in a set \(D\) a unique real number denoted by \(f(x, y)\). The set \(D\) is the domain of \(f\) and its range is the set of values that \(f\) takes on, that is, \(f(x, y) \mid (x, y) \in D\).

Example

• Volume of a cylinder \(V(r,h) = \pi r^2 h\)
• Area of rectangle \(A(l,b) = lb\)