Section_2.1-What Is a Function

Section_2.1-What Is a Function - Section 2.1 What Is a...

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Section 2.1 What Is a Function? DEFINITION: A function f is a rule that assigns to each element x in a set A exactly one element, called f ( x ) , in a set B . The set A is called the domain of f. The range of f is the set of all possible values of f ( x ) as x varies throughout the domain. EXAMPLES: 1. Let f ( x ) = x + x. Then f (0) = 0 + 0 = 0 f (4) = 4 + 4 = 6 2. Let f ( x ) = 3 x 2 + x - 5 . Then f ( - 2) = 3 · ( - 2) 2 + ( - 2) - 5 = 5 f (0) = 3 · 0 2 + 0 - 5 = - 5 f (4) = 3 · 4 2 + 4 - 5 = 47 f ( 1 2 ) = 3 · ( 1 2 ) 2 + 1 2 - 5 = - 15 4 3. Let f ( x ) = x + 1 x . Then f (3) = 3 + 1 3 = 4 3 = 2 3 f (5) = 5 + 1 5 = 6 5 and f ( a - 1) = a - 1 + 1 a - 1 = a a - 1 4. Let f ( x ) = { 3 x 2 + x - 5 if x 0 x + x if x > 0 and g ( x ) = { 3 x 2 + x - 5 if x < 0 x + x if x 0 Then f ( - 2) = 3 · ( - 2) 2 + ( - 2) - 5 = 5 f (0) = 3 · 0 2 + 0 - 5 = - 5 f (4) = 4 + 4 = 6 and g ( - 2) = 3 · ( - 2) 2 + ( - 2) - 5 = 5 g (0) = 0 + 0 = 0 g (4) = 4 + 4 = 6 1

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Section_2.1-What Is a Function - Section 2.1 What Is a...

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