Unformatted text preview: MATH 31102 Notes Introduction to Higher Math 1 Function Attributes and Properties If a function is defined as f : A → B , then the set A is called the domain of f ; the set B is the codomain of f . We might be curious about which elements of B are actually achieved by f ; i.e., which y ∈ B are such that for some x in A , f ( x ) = y ? We might call this set the image or range . Put in glorious setbuilderandlogic notation, the image of a function f : A → B is { y ∈ B : ∃ x ∈ A,f ( x ) = y } We might look at a simple example: consider a function f : { 1 , 2 , 3 , 4 , 5 } → { 1 , 2 , 3 } such that f (1) = 2, f (2) = 3, f (3) = 3, f (4) = 2, and f (5) = 2. Alternatively, we might describe f as { (1 , 2) , (2 , 3) , (3 , 3) , (4 , 2) , (5 , 2) } . Then, as stated in the declaration of f , f has domain { 1 , 2 , 3 , 4 , 5 } and codomain { 1 , 2 , 3 } . The image of f is the set of second coordinates actually appearing in f , which is { 2 , 3 } — note that this is not quite the entire codomain.— note that this is not quite the entire codomain....
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This note was uploaded on 01/12/2012 for the course MATH 311 taught by Professor Staff during the Spring '08 term at University of Louisville.
 Spring '08
 Staff
 Math

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