Alg_Complete_Practice (1)

# Alg_Complete_Practice (1) - COLLEGE ALGEBRA Practice...

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COLLEGE ALGEBRA Practice Problems Paul Dawkins

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College Algebra Table of Contents Preface ........................................................................................................................................... iii Outline ........................................................................................................................................... iv Preliminaries .................................................................................................................................. 6 Introduction ................................................................................................................................................ 6 Integer Exponents ...................................................................................................................................... 6 Rational Exponents .................................................................................................................................... 7 Real Exponents .......................................................................................................................................... 8 Radicals ...................................................................................................................................................... 9 Polynomials ............................................................................................................................................... 10 Factoring Polynomials .............................................................................................................................. 10 Rational Expressions ................................................................................................................................. 12 Complex Numbers .................................................................................................................................... 13 Solving Equations and Inequalities ............................................................................................ 13 Introduction ............................................................................................................................................... 13 Solutions and Solution Sets ....................................................................................................................... 14 Linear Equations ....................................................................................................................................... 15 Application of Linear Equations ............................................................................................................... 15 Equations With More Than One Variable ................................................................................................. 16 Quadratic Equations – Part I ..................................................................................................................... 16 Quadratic Equations – Part II .................................................................................................................... 17 Solving Quadratic Equations : A Summary .............................................................................................. 18 Application of Quadratic Equations .......................................................................................................... 18 Equations Reducible to Quadratic Form ................................................................................................... 19 Equations with Radicals ............................................................................................................................ 19 Linear Inequalities ..................................................................................................................................... 20 Polynomial Inequalities ............................................................................................................................. 20 Rational Inequalities ................................................................................................................................. 20 Absolute Value Equations ......................................................................................................................... 21 Absolute Value Inequalities ...................................................................................................................... 22 Graphing and Functions ............................................................................................................. 22 Introduction ............................................................................................................................................... 22 Graphing ................................................................................................................................................... 23 Lines .......................................................................................................................................................... 24 Circles ....................................................................................................................................................... 24 The Definition of a Function ..................................................................................................................... 25 Graphing Functions ................................................................................................................................... 27 Combining Functions ................................................................................................................................ 27 Inverse Functions ...................................................................................................................................... 28 Common Graphs ......................................................................................................................... 28 Introduction ............................................................................................................................................... 28 Lines, Circles and Piecewise Functions .................................................................................................... 29 Parabolas ................................................................................................................................................... 29 Ellipses ...................................................................................................................................................... 30 Hyperbolas ................................................................................................................................................ 30 Miscellaneous Functions ........................................................................................................................... 31 Transformations ........................................................................................................................................ 31 Symmetry .................................................................................................................................................. 32 Rational Functions .................................................................................................................................... 32 Polynomial Functions .................................................................................................................. 32 Introduction ............................................................................................................................................... 32 Dividing Polynomials ............................................................................................................................... 33 Zeroes/Roots of Polynomials .................................................................................................................... 34 © 2007 Paul Dawkins i