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UC11A-1.2 - Math 11A Calculus w Applications I Text...

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Math 11A - Calculus w/ Applications I Text: Neuhauser, , 2nd edition Calculus for Biology and Medicine 1.2 Elementary Functions 1.2.1 What is a function? Definition: a is a rule that assigns each element in a set (called function B E the ) exactly one element in the set (the ). The domain codomain C F image range of is denoted ; the of is in }. B C œ 0 B 0 œ Ö0 B lB E a b a b Note: two functions are equal IFF (if and only if) 1. and have the same domain. 0 1 2. for all in the domain. 0 B œ 1 B B a b a b example: for a. b. 0 B œ #B  ' B − Ò!ß &Ó B − a b example: and 0 B œ B 1 B œ B a b a b È # Definition: a function is: if ; if even odd 0  B œ 0 B 0  B œ  0 B Þ a b a b a b a b Definition: the of functions is denoted for composition 0 ‰ 1 B œ 0 1ÐBÑ a b a b each in the domain of for which is in the domain of . B 1 1 B 0 a b example: ; 0 B œ B  # 1 B œ B  * a b a b È # Basic functions: 1.2.2 Polynomial functions -- of form +  + B  + B  Þ Þ Þ  + B ! " # 8 # 8 1.2.3 Rational functions -- of form where and are 0 B œ : ; a b
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