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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