MULTIVARIABLE FUNCTIONS

MULTIVARIABLE FUNCTIONS

1. TWO VARIABLES

   • Let D be a set of ordered pair of real numbers. If for each ordered pair (x,y) of D, corresponds a unique real number f(x,y), then it is said that f is a function of x and y.
     • DOMAIN AND RANGE
       • The set D is the domain of f, and the correspondent set of values f(x,y) is the range of f.
     • VARIABLES
       • For the function z=f(x,y) x and y are the independent variables, z is the dependent variable.

2. THREE VARIABLES

   • Let D be a set of triples of real numbers. If for triple (x,y,z) of D, corresponds a unique real number f(x,y,z), then it is said that f is a function of x, y, and z.
     • DOMAIN AND RANGE
       • The set D is the domain of f, and the correspondent set of values f(x,y,z) is the range of f.
     • VARIABLES
       • For the function w=f(x,y,z) x , y, and z are the independent variables, w is the dependent variable.