Lect3A - Functions Definition: Examples: a) Graphs: y 4 A...

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92.131 Lecture 3A 1 of 22 Ronald Brent © 2010 All rights reserved. x y −4 −2 2 4 2 2 4 Functions Definition: A function f , defined from a set A to a set B , is a rule that associates with each element of the set A one, and only one, element of the set B . Examples: a) Graphs: b) Tables: c) Words: The cost of a taxicab is $2.00 for the first 1/4 of a mile and $1.00 for each additional 1/8 of a mile. d) Symbols: 2 ) ( 2 + = x x f x y 0 50 10 57.50 20 65 30 80 40 95 50 125 60 200
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92.131 Lecture 3A 2 of 22 Ronald Brent © 2010 All rights reserved. x y −4 −2 2 4 2 4 Definition: The set A of all inputs is called the domain , and the set B of all outputs is called the range . Example: Example: Domain 4 4 x Range 4 0 x D o m a i n {0, 10, 20, 30, 40, 50, 60} Range {50, 57.5, 65, 80, 95, 125, 200} Example: 2 ) ( 2 + = x x f Domain All real x or ) , ( Range All real 2 y or ) , 2 [ x y 0 50 10 57.50 20 65 30 80 40 95 50 125 60 200
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92.131 Lecture 3A 3 of 22 Ronald Brent © 2010 All rights reserved. Graphs Definition: The Cartesian (rectangular) coordinate plane consists of ordered pairs of numbers ( x , y ), or points, where the value of x indicates the horizontal position of the point and the y value refers to the vertical position. Coordinate Axes x -axis Points ( a , 0) y -axis Points (0, b ) II I Quadrants: I All points ( a , b ) with a > 0 and b > 0. II All points ( a , b ) with a < 0 and b > 0. III All points ( a , b ) with a < 0 and b < 0. III IV IV All points ( a , b ) with a > 0 and b < 0. x ( a , b ) b a y
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92.131 Lecture 3A 4 of 22 Ronald Brent © 2010 All rights reserved. x -5 -4 -3 -2 -1 1 2 3 4 5 y 0 1 2 3 4 5 Example: ( 4, 4) ( 3, 2) ( 0 , 4) ( 3 , 4) ( 3 , 0) (4, 2)
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92.131 Lecture 3A 5 of 22 Ronald Brent © 2010 All rights reserved. x -4 -3 -2 -1 0 1 2 3 4 f ( x ) 0 2 4 6 8 10 12 14 16 Graphs of Functions Definition: The graph of a function ( or equation) ) ( x f y = is the set of points ( x , y ) that satisfy the function (equation). Example: 2 ) ( x x f = x y -4 16 -3.5 12.25 -3 9 -2.5 6.25 -2 4 -1.5 2.25 -1 1 -0.5 .25 0 0 0.5 .25 1 1 1.5 2.25 2 4 2.5 6.25 3 9 3.5 12.25 4 16
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92.131 Lecture 3A 6 of 22 Ronald Brent © 2010 All rights reserved. Elementary Functions 1) Polynomial Ex: 1 ) ( 2 = x x f or 4 2 ) ( 2 3 + + = x x x x f 2) Rational Ex: 1 2 1 ) ( 2 3 + + = x x x x f or 4 8 10 3 4 1 ) ( x x x x x f + = 3) Algebraic Ex: 2 ) ( 2 + = x x f or 5 2 1 ) ( 2 3 + + = x x x x x f 4) Exponential Ex: x x f 2 ) ( = or x e x f = ) ( 5) Logarithmic Ex: ) ( ln ) ( x x f = or ) ( log ) ( 2 x x f = 6) Trigonometric Ex: x x f sin ) ( = or x x f cos ) ( =
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92.131 Lecture 3A 7 of 22 Ronald Brent © 2010 All rights reserved.
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This note was uploaded on 02/13/2012 for the course MATH 92.131 taught by Professor Staff during the Fall '09 term at UMass Lowell.

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Lect3A - Functions Definition: Examples: a) Graphs: y 4 A...

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