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Unformatted text preview: Supplemental Lecture 1 Continuity and Limits I  2 Functions • Let X and Y be sets, and let f ⊆ X × Y . – That means that f is a set of ordered pairs ( x , y ) such that x ∈ X and y ∈ Y . • If f also satisfies the property that for all x ∈ X there exists a unique y ∈ Y such that ( x , y ) ∈ f , then f is a function . I  3 Function Notation • We write f : X → Y . • X is called the domain of f , and Y is called the range of f . • If ( x , y ) ∈ f , then we write y = f ( x ) and y is called the image of x under f . I  4 The Absolute Value Function • The absolute value function · : R → R + = [0, ∞ ) will play an essential role. • For x ∈ R , • Properties of absolute value: a)  xy  =  x  y  b)  x    y  ≤ x + y  ≤  x  +  y  (Triangle Inequality) . < ≥ = x x x x x10.5 0.5 1 0.2 0.4 0.6 0.8 1 I  5 Definition of Continuity in One Dimension • Let x ∈ D and y = f ( x )....
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This note was uploaded on 01/09/2011 for the course ECON 7230 taught by Professor Feigenbaum during the Spring '10 term at Utah Valley University.
 Spring '10
 Feigenbaum
 Macroeconomics

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