10.1 - Functions of Two or More Independent Variables
y  f (x )

1 independent variable (x), 1 dependent variable (y)
Domain: set of all possible x-values (input)
Range: set of all possible y-values (output)
------------------------------------------------------------------------------------------------------------z  f ( x, y )

2 independent variables (x and y), 1 dependent variable (z)
Domain: ordered pairs ( x, y )
Range: z  f ( x, y )
-----------------------------------------------------------------------------------------------------------Generalize to functions whose domain is made up of ordered n-tuples ( x1 , x 2 , ... , x n ) and range
f ( x1 , x 2 , ... , xn ).
EX: (#7) Evaluate
f ( x, y )  2 x  3 y 2
EX: (#14) Find the largest domain for
at (- 1, 2).
f ( x, y ) 
9  x2  y 2
.
Surfaces: Read p. 506-507 concerning surfaces and the figures 10.7, 10.8, 10.9 and 10.10.
Level curves and Contour lines
- level curves are drawn in the function domain
- contour lines are drawn on the surface of the graph
Definition: Suppose that f : D   and D   2 . Then the level curves of f comprise the set of all
points ( x, y ) in the x-y plane such that f is constant. ( f ( x, y )  c )
(Note: To get good information from the graphs of level curves, choose equidistant values for c.)
Back to #14: Determine the equation of the level curves f ( x, y )  c together with possible values of c.