algebra_of_functions - Algebra of Functions 1999 by Design...

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©1999 by Design Science, Inc. Algebra of Functions
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©1999 by Design Science, Inc. 2 Objectives To define the sum, difference, product, and quotient of functions. To form and evaluate composite functions.
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©1999 by Design Science, Inc. 3 Basic function operations Sum Difference Product Quotient ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 , 0 f x f f g x x g x g g x = = ( 29 ( 29 ( 29 ( 29 f g x f x g x = + + ( 29 ( 29 ( 29 ( 29 & f g x f x g x = ( 29 ( 29 ( 29 ( 29 f g x f x g x = g g
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©1999 by Design Science, Inc. 4 Function, domain, & range The domain of a function is the set of all “first coordinates” of the ordered pairs of a relation. The range of a function is the set of all “second coordinates” of the ordered pairs of a relation. A relation is a function if all values of the domain are unique (they do not repeat). A test to see if a relation is a function is the vertical line test . If it is possible to draw a vertical line and cross the graph of a relation in more than one point, the relation is not a function.
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©1999 by Design Science, Inc. 5 Example 1 Find each function and state its domain: f + g f g f · g f / g ( 29 ( 29 ; 1 1 g x f x x x + = - = ( 29 ( 29 { } 1
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This note was uploaded on 01/12/2011 for the course MAT 1117 MAT 117 taught by Professor White during the Spring '09 term at University of Phoenix.

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algebra_of_functions - Algebra of Functions 1999 by Design...

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