College Algebra - stitz-zeager.com

1 College AlgebraVersionb cCorrected EditionbyCarl Stitz, Zeager, Community College Lorain County Community CollegeJuly 4, 2013iiAcknowledgementsWhile the cover of this textbook lists only two names, the book as it stands today would simplynot exist if not for the tireless work and dedication of several people. First and foremost, we wishto thank our families for their patience and support during the creative process. We would alsolike to thank our students - the sole inspiration for the work. Among our colleagues, we wish tothank Rich Basich, Bill Previts, and Irina Lomonosov, who not only were early adopters of thetextbook, but also contributed materials to the project.

2 Special thanks go to Katie Cimperman,Terry Dykstra, Frank LeMay, and Rich Hagen who provided valuable feedback from the also to David Stumpf, Ivana Gorgievska, Jorge Gerszonowicz, Kathryn Arocho, HeatherBubnick, and Florin Muscutariu for their unwaivering support (and sometimes defense) of thebook. From outside the classroom, we wish to thank Don Anthan and Ken White, who designedthe electric circuit applications used in the text, as well as Drs. Wendy Marley and Marcia Ballingerfor the Lorain CCC enrollment data used in the text. The authors are also indebted to the goodfolks at our schools bookstores, Gwen Sevtis (Lakeland CC) and Chris Callahan (Lorain CCC),for working with us to get printed copies to the students as inexpensively as possible.

3 We wouldalso like to thank Lakeland folks Jeri Dickinson, Mary Ann Blakeley, Jessica Novak, and CorrieBergeron for their enthusiasm and promotion of the project. The administrations at both schoolshave also been very supportive of the project, so from Lakeland, we wish to thank Dr. Morris , Jr., President, Dr. Fred Law, Provost, Deans Don Anthan and Dr. Steve Oluic, and theBoard of Trustees. From Lorain County Community College , we wish to thank Dr. Roy A. Church,Dr. Karen Wells, and the Board of Trustees. From the Ohio Board of Regents, we wish to thankformer Chancellor Eric Fingerhut, Darlene McCoy, Associate Vice Chancellor of Affordability andEfficiency, and Kelly Bernard.

4 From OhioLINK, we wish to thank Steve Acker, John Magill, andStacy Brannan. We also wish to thank the good folks at WebAssign, most notably Chris Hall,COO, and Joel Hollenbeck (former VP of Sales.) Last, but certainly not least, we wish to thankall the folks who have contacted us over the interwebs, most notably Dimitri Moonen and JoelWordsworth, who gave us great feedback, and Antonio Olivares who helped debug the source of ContentsPrefaceix1 Relations and of Real Numbers and the Cartesian Coordinate Plane .. of Numbers .. Cartesian Coordinate Plane.

5 In the Plane .. of Equations .. to Functions .. Notation .. with Functions .. Arithmetic .. of Functions .. Function Behavior .. 144ivTable of Contents2 Linear and Quadratic Functions .. Value Functions .. Functions .. with Absolute Value and Quadratic Functions .. 2333 Polynomial of Polynomials .. Factor Theorem and the Remainder Theorem .. Zeros of Polynomials .. Those Wishing to use a Graphing Calculator .. Those Wishing NOT to use a Graphing Calculator .. Zeros and the Fundamental Theorem of Algebra .

6 2974 Rational to Rational Functions .. of Rational Functions .. Inequalities and Applications .. 353 Table of .. 3565 Further Topics in Composition .. Functions .. Algebraic Functions .. 4116 Exponential and Logarithmic to Exponential and Logarithmic Functions .. of Logarithms .. Equations and Inequalities .. Equations and Inequalities .. of Exponential and Logarithmic Functions .. of Exponential Functions .. of Logarithms .. 4907 Hooked on to Conics .. 527viTable of .. 5448 Systems of Equations and of Linear Equations: Gaussian Elimination.

7 Of Linear Equations: Augmented Matrices .. Arithmetic .. of Linear Equations: Matrix Inverses .. and Cramer s Rule .. and Properties of the Determinant .. s Rule and Matrix Adjoints .. Fraction Decomposition .. of Non-Linear Equations and Inequalities .. 6489 Sequences and the Binomial .. Notation .. Induction .. Answers .. Binomial Theorem .. 692 PrefaceThank you for your interest in our book, but more importantly, thank you for taking the time toread the Preface. I always read the Prefaces of the textbooks which I use in my classes becauseI believe it is in the Preface where I begin to understand the authors - who they are, what theirmotivation for writing the book was, and what they hope the reader will get out of reading thetext.

8 Pedagogical issues such as content organization and how professors and students should bestuse a book can usually be gleaned out of its Table of Contents, but the reasons behind the choicesauthors make should be shared in the Preface. Also, I feel that the Preface of a textbook shoulddemonstrate the authors love of their discipline and passion for teaching, so that I come awaybelieving that they really want to help students and not just make money. Thus, I thank my fellowPreface-readers again for giving me the opportunity to share with you the need and vision whichguided the creation of this book and passion which both Carl and I hold for Mathematics and theteaching of and I are natives of Northeast Ohio.

9 We met in graduate school at Kent State Universityin 1997. I finished my in Pure Mathematics in August 1998 and started teaching at LorainCounty Community College in Elyria, Ohio just two days after graduation. Carl earned his inPure Mathematics in August 2000 and started teaching at Lakeland Community College in Kirtland,Ohio that same month. Our schools are fairly similar in size and mission and each serves a similarpopulation of students. The students range in age from about 16 (Ohio has a Post-SecondaryEnrollment Option program which allows high school students to take College courses for free whilestill in high school.)

10 To over 65. Many of the non-traditional students are returning to school inorder to change careers. A majority of the students at both schools receive some sort of financialaid, be it scholarships from the schools foundations, state-funded grants or federal financial aidlike student loans, and many of them have lives busied by family and job demands. Some willbe taking their Associate degrees and entering (or re-entering) the workforce while others will becontinuing on to a four-year College or university. Despite their many differences, our studentsshare one common attribute: they do not want to spend$200 on a College Algebra challenge of reducing the cost of textbooks is one that many states, including Ohio, are takingquite seriously.