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COLLEGE ALGEBRAPaul Dawkins
College AlgebraTable of ContentsPreface . iiiOutline . ivPreliminaries . 1Introduction . 1Integer Exponents . 2Rational Exponents . 9Real Exponents .15Radicals .16Polynomials.25Factoring Polynomials .31Rational Expressions .41Complex Numbers .52Solving Equations and Inequalities. 58Introduction .58Solutions and Solution Sets .59Linear Equations .63Application of Linear Equations .71Equations With More Than One Variable .81Quadratic Equations – Part I .85Quadratic Equations – Part II .93Solving Quadratic Equations : A Summary .104Application of Quadratic Equations .107Equations Reducible to Quadratic Form .111Equations with Radicals .116Linear Inequalities.122Polynomial Inequalities .129Rational Inequalities .135Absolute Value Equations .140Absolute Value Inequalities .147Graphing and Functions . 152Introduction .152Graphing .153Lines .159Circles .169The Definition of a Function .175Graphing Functions .188Combining Functions .192Inverse Functions .199Common Graphs . 206Introduction .206Lines, Circles and Piecewise Functions .207Parabolas .208Ellipses .218Hyperbolas .222Miscellaneous Functions .226Transformations .229Symmetry .235Rational Functions .240Polynomial Functions . 246Introduction .246Dividing Polynomials .247Zeroes/Roots of Polynomials .252 2007 Paul Dawkinsihttp://tutorial.math.lamar.edu/terms.aspx
College AlgebraGraphing Polynomials .257Finding Zeroes of Polynomials .265Partial Fractions .273Exponential and Logarithm Functions . 281Introduction .281Exponential Functions .282Logarithm Functions .287Solving Exponential Equations .297Solving Logarithm Equations .304Applications .310Systems of Equations. 317Introduction .317Linear Systems with Two Variables .318Linear Systems with Three Variables .326Augmented Matrices .330More on the Augmented Matrix .339Non-Linear Systems .345 2007 Paul Dawkinsiihttp://tutorial.math.lamar.edu/terms.aspx
College AlgebraPrefaceHere are my online notes for my Algebra course that I teach here at Lamar University, although Ihave to admit that it’s been years since I last taught this course. At this point in my career Imostly teach Calculus and Differential Equations.Despite the fact that these are my “class notes”, they should be accessible to anyone wanting tolearn Algebra or needing a refresher for algebra. I’ve tried to make the notes as self contained aspossible and do not reference any book. However, they do assume that you’ve had someexposure to the basics of algebra at some point prior to this. While there is some review ofexponents, factoring and graphing it is assumed that not a lot of review will be needed to remindyou how these topics work.Here are a couple of warnings to my students who may be here to get a copy of what happened ona day that you missed.1. Because I wanted to make this a fairly complete set of notes for anyone wanting to learnalgebra I have included some material that I do not usually have time to cover in classand because this changes from semester to semester it is not noted here. You will need tofind one of your fellow class mates to see if there is something in these notes that wasn’tcovered in class.2. Because I want these notes to provide some more examples for you to read through, Idon’t always work the same problems in class as those given in the notes. Likewise, evenif I do work some of the problems in here I may work fewer problems in class than arepresented here.3. Sometimes questions in class will lead down paths that are not covered here. I try toanticipate as many of the questions as possible in writing these up, but the reality is that Ican’t anticipate all the questions. Sometimes a very good question gets asked in classthat leads to insights that I’ve not included here. You should always talk to someone whowas in class on the day you missed and compare these notes to their notes and see whatthe differences are.4. This is somewhat related to the previous three items, but is important enough to merit itsown item. THESE NOTES ARE NOT A SUBSTITUTE FOR ATTENDING CLASS!!Using these notes as a substitute for class is liable to get you in trouble. As already notednot everything in these notes is covered in class and often material or insights not in thesenotes is covered in class. 2007 Paul x
College AlgebraOutlineHere is a listing of all the material that is currently available in these notes.PreliminariesInteger Exponents – In this section we will start looking at exponents and theirproperties.Rational Exponents – We will define rational exponents in this section and extend theproperties from the previous section to rational exponents.Real Exponents – This is a short acknowledgment that the exponent properties from theprevious two sections will hold for any real exponent.Radicals – Here we will define radical notation and relate radicals to rational exponents.We will also give the properties of radicals.Polynomials – We will introduce the basics of polynomials in this section includingadding, subtracting and multiplying polynomials.Factoring Polynomials – This is the most important section of all the preliminaries.Factoring polynomials will appear in pretty much every chapter in this course. Withoutthe ability to factor polynomials you will be unable to complete this course.Rational Expressions – In this section we will define rational expressions and di
learn Algebra or needing a refresher for algebra. I’ve tried to make the notes as self contained as possible and do not reference any book. However, they do assume that you’ve had some exposure to the basics of algebra at some point prior to this. While there is some review of
