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handout 14-1 - Math 200 Spring 2010 Handout 10 Section 14-1...

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Math 200, Spring 2010 Handout 10 Section 14-1 Functions of Two or More Variables Definition of a Function f of Two Variables and the Graph of f 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, range = ( ) ( ) { } , | , f x y x y D . If f is a function of two variables with domain D , then the graph of f is the set of all points ( ) , , x y z in 3 such that ( ) , z f x y = and ( ) , x y is in D . The graph of f is a surface S lying directly above or below its domain D in the xy -plane. 1. Find the domains and ranges of the following functions and sketch their domains. (a) ( ) 2 , 1 f x y x y = + (b) ( ) ( ) , ln f x y y x y x = + (c) 2 1 ( , ) g y z z y = + (d) / ( , ) r s P r s e = Horizontal and Vertical Traces of the Graph of Function f ( x , y ) Traces are curves obtained by intersecting the graph of a function ( ) , f x y with planes parallel to a coordinate plane.
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