precalculus - s lculus P re recalculus P recalcu P...

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Unformatted text preview: s lculus P re recalculus P recalcu P recalculus culus alculus P recalc lus P r calculus P recal P ecalculus ulus P recalculu P reca P rec P recalcul us David A. Santos dsantos@ccp.edu January 2, 2010 VERSION ii Copyright c circlecopyrt 2007 David Anthony SANTOS. Permission is granted to copy, distribute and/or modify this docu-ment under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. iii Contents Preface v To the Student viii 1 The Line 1 1.1 Sets and Notation . . . . . . . . . . . . . . . 1 Homework . . . . . . . . . . . . . . . . . . 5 1.2 Rational Numbers and Irrational Numbers . . 5 Homework . . . . . . . . . . . . . . . . . . 8 1.3 Operations with Real Numbers . . . . . . . . 9 Homework . . . . . . . . . . . . . . . . . . 13 1.4 Order on the Line . . . . . . . . . . . . . . . 14 Homework . . . . . . . . . . . . . . . . . . 18 1.5 Absolute Value . . . . . . . . . . . . . . . . 19 Homework . . . . . . . . . . . . . . . . . . 21 1.6 Completeness Axiom . . . . . . . . . . . . . 22 2 The Plane 24 2.1 Sets on the Plane . . . . . . . . . . . . . . . 24 Homework . . . . . . . . . . . . . . . . . . 26 2.2 Distance on the Real Plane . . . . . . . . . . 26 Homework . . . . . . . . . . . . . . . . . . 28 2.3 Circles . . . . . . . . . . . . . . . . . . . . . 29 Homework . . . . . . . . . . . . . . . . . . 31 2.4 Semicircles . . . . . . . . . . . . . . . . . . 32 Homework . . . . . . . . . . . . . . . . . . 33 2.5 Lines . . . . . . . . . . . . . . . . . . . . . 33 Homework . . . . . . . . . . . . . . . . . . 36 2.6 Parallel and Perpendicular Lines . . . . . . . 37 Homework . . . . . . . . . . . . . . . . . . 42 2.7 Linear Absolute Value Curves . . . . . . . . 43 Homework . . . . . . . . . . . . . . . . . . 45 2.8 Parabolas, Hyperbolas, and Ellipses . . . . . 45 Homework . . . . . . . . . . . . . . . . . . 49 3 Functions 50 3.1 Basic Definitions . . . . . . . . . . . . . . . 50 Homework . . . . . . . . . . . . . . . . . . 55 3.2 Graphs of Functions and Functions from Graphs 56 Homework . . . . . . . . . . . . . . . . . . 59 3.3 Natural Domain of an Assignment Rule . . . 60 Homework . . . . . . . . . . . . . . . . . . 62 3.4 Algebra of Functions . . . . . . . . . . . . . 63 Homework . . . . . . . . . . . . . . . . . . 68 3.5 Iteration and Functional Equations . . . . . . 70 Homework . . . . . . . . . . . . . . . . . . 72 3.6 Injections and Surjections . . . . . . . . . . . 72 Homework . . . . . . . . . . . . . . . . . . 77 3.7 Inversion . . . . . . . . . . . . . . . . . . . 77 Homework . . . . . . . . . . . . . . . . . . 82 4 Transformations of the Graph of Functions 84 4.1 Translations . . . . . . . . . . . . . . . . . . 84 Homework . . . . . . . . . . . . . . . . . . 86 4.2 Distortions . . . . . . . . . . . . . . . . . . . ....
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