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Contents

Preface ........................................................................................................................................... iii 



Outline ........................................................................................................................................... iv 



Preliminaries .................................................................................................................................. 1 



Introduction  ................................................................................................................................................ 1 



Integer Exponents ...................................................................................................................................... 2 



Rational Exponents .................................................................................................................................... 9 



Real Exponents ........................................................................................................................................ 15 



Radicals .................................................................................................................................................... 16 



Polynomials .............................................................................................................................................. 25 



Factoring Polynomials ............................................................................................................................. 31 



Rational Expressions ................................................................................................................................ 41 



Complex Numbers ................................................................................................................................... 52 



Solving Equations and Inequalities ............................................................................................ 58 



Introduction  .............................................................................................................................................. 58 



Solutions and Solution Sets ...................................................................................................................... 59 



Linear Equations ...................................................................................................................................... 63 



Application of Linear Equations .............................................................................................................. 71 



Equations With More Than One Variable ................................................................................................ 81 



Quadratic Equations – Part I .................................................................................................................... 85 



Quadratic Equations – Part II ................................................................................................................... 93 



Solving Quadratic Equations : A Summary ............................................................................................104 



Application of Quadratic Equations ........................................................................................................107 



Equations Reducible to Quadratic Form .................................................................................................111 



Equations with Radicals ..........................................................................................................................116 



Linear Inequalities ...................................................................................................................................122 



Polynomial Inequalities  ...........................................................................................................................129 



Rational Inequalities ...............................................................................................................................135 



Absolute Value Equations .......................................................................................................................140 



Absolute Value Inequalities ....................................................................................................................147 



Graphing and Functions ........................................................................................................... 152 



Introduction  .............................................................................................................................................152 



Graphing .................................................................................................................................................153 



Lines ........................................................................................................................................................159 



Circles .....................................................................................................................................................169 



The Definition of a Function ...................................................................................................................175 



Graphing Functions .................................................................................................................................186 



Combining Functions ..............................................................................................................................190 



Inverse Functions ....................................................................................................................................197 



Common Graphs ....................................................................................................................... 204 



Introduction  .............................................................................................................................................204 



Lines, Circles and Piecewise Functions ..................................................................................................205 



Parabolas .................................................................................................................................................206 



Ellipses ....................................................................................................................................................216 



Hyperbolas ..............................................................................................................................................220 



Miscellaneous Functions .........................................................................................................................224 



Transformations ......................................................................................................................................227 



Symmetry ................................................................................................................................................233 



Rational Functions ..................................................................................................................................238 



Polynomial Functions ................................................................................................................ 244 



Introduction  .............................................................................................................................................244 



Dividing Polynomials..............................................................................................................................245 



Zeroes/Roots of Polynomials ..................................................................................................................250 College Algebra



© 2007 Paul Dawkins  ii   



Graphing Polynomials .............................................................................................................................255 



Finding Zeroes of Polynomials ...............................................................................................................263 



Partial Fractions ......................................................................................................................................271 



Exponential and Logarithm Functions .................................................................................... 279 



Introduction  .............................................................................................................................................279 



Exponential Functions .............................................................................................................................280 



Logarithm Functions ...............................................................................................................................285 



Solving Exponential Equations ...............................................................................................................295 



Solving Logarithm Equations .................................................................................................................302 



Applications ............................................................................................................................................308 



Systems of Equations ................................................................................................................. 315 



Introduction  .............................................................................................................................................315 



Linear Systems with Two Variables .......................................................................................................316 



Linear Systems with Three Variables .....................................................................................................324 



Augmented Matrices ...............................................................................................................................326 



More on the Augmented Matrix ..............................................................................................................335 



Non-Linear Systems ................................................................................................................................341