Functions of Several Variables

Basic Notation

• f(x) represents a function in terms of x.
  • Example: y = 4x² (where y = f(x)).
• Z = f(x, y) represents a function of two variables.
  • Example: Area of a triangle A = 0.5 * base * height → f(b, h) = 0.5bh.

Important Terms

• Dependent Variable: Z (or the function output).
• Independent Variables: x and y (or the function inputs).
  • We might also work with three variables, e.g., f(x, y, z).

Domain of a Function

• Definition: The set of all possible values of the independent variables.
• Example: For f(x, y) = ln(xy), the domain is where xy > 0.
  • Can be expressed with:
    1. Graphical representation: 1st and 3rd quadrants, excluding axes.
    2. Words: