{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

handout 14-1

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

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}