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Unformatted text preview: Math021, week 1 Functions and their Graphs Definition 1.1 A function f is a rule assigning a number to each of the num bers. The number assigned to the number x via the rule f is usually denoted by f ( x ) . Remark 1.2 The objective of our course “Calculus” is to study functions. Example 1.3 Let f be the rule of assignment so that for each number x , its square x 2 is assigned. The handy notation to define this function is to write f ( x ) = x 2 for all x . Example 1.4 Similarly, 1. g ( x ) =  x  for all x . 2. h ( x ) = 1 + x 4 for all x . are example of functions. However, 1. p ( x ) = 1 x 2. q ( x ) = √ x are somewhat different because they do not assign a number to EVERY choice of a number. Definition 1.5 The domain of a function f is the collection of numbers x such that a number is assigned to x via the rule f (we also say that f ( x ) is defined). Example 1.6 The domain of the function p ( x ) = 1 x is the collection of all numbers except . Example 1.7 The domain of the function q ( x ) = √ x is the collection of all nonnegative numbers. Definition 1.8 Two coordinateaxes in the plane are two straight lines perpen dicular to each other. One of them is usually called the “xaxis”, another line is usually called the “yaxis”. For every pointusually called the “yaxis”....
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 Fall '10
 LUXNU
 Calculus

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