Huettenmueller - College Algebra Demystified.pdf - Algebra & Trigonometry - Kuya

COLLEGEALGEBRA

DEMYSTIFIED

Rhonda Huettenmueller

McGRAW-HILL

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DOI: 10.1036/0071439285

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CONTENTS

Preface

vii

CHAPTER 1

Completing the Square

CHAPTER 2

Absolute Value Equations and

Inequalities

CHAPTER 3

The xy Coordinate Plane

CHAPTER 4

Lines and Parabolas

CHAPTER 5 Nonlinear Inequalities

124

CHAPTER 6

Functions

148

CHAPTER 7

Quadratic Functions

199

CHAPTER 8

Transformations and Combinations

219

CHAPTER 9

Polynomial Functions

278

CHAPTER 10 Systems of Equations and Inequalities 354

CHAPTER 11 Exponents and Logarithms

402

Final Exam

432

Index

443

PREFACE

Early in my teaching career, I realized two seemingly contradictory facts—

that students are fully capable of understanding mathematical concepts but

that many have had little success with mathematics. There are several reasons

people struggle with mathematics. One is a weak background in basic mathe-

matics. Most topics in mathematics are sequential. Weaknesses in any area

will likely cause problems later. Another is that textbooks tend to present

too many concepts at once, keeping students from being able to absorb

them. I wrote this book (as well as my previous book, Algebra

Demystiﬁed) with these issues in mind. Each section is short, containing

exactly one new concept. This gives you a chance to absorb the material.

Also, I have included detailed examples and solutions so that you can con-

centrate on the new lesson without being distracted by missing steps. The

extra detail will also help you to review important skills.

You will get the most out of this book if you work on it several times a

week, a little at a time. Before working on a new section, review the previous

sections. Most sections expand on the ideas in previous sections. Study for

the end-of-chapter reviews and ﬁnal exam as you would a regular test. This

will help you to see the big picture. Finally, study the graphs and their

equations. Even with graphing calculators to plot graphs, it is important in

college algebra and more advanced courses to understand why graphs behave

the way they do. Because testing has become so important, I would like to

leave you with a few tips on how to study for and to take a mathematics test.

* Study at regular, frequent intervals. Do not cram.

* Prepare one sheet of notes as if you were allowed to bring it into the

test. This exercise will force you to summarize the concepts and to

focus on what is important.

vii

viii

PREFACE

* Imagine explaining the material to someone else. You will have mas-

tered the material only when you can explain it in your own words.

* When taking a test, read it over before answering any questions.

Answer the easy questions ﬁrst. By the time you get to the more di-

cult problems, your mind will already be thinking mathematically.

Also, this can keep you from spending too much valuable test time

on harder problems.

* Be patient with yourself while you are learning. Understanding will not

come all at once. But it will come.

Acknowledgments

I am very grateful to my family for tolerating my neglect while ﬁnishing this

book. I also want to express my appreciation to my friends at the University

of North Texas for their encouragement. In particular, I want to thank my

colleague Mary Ann Teel for her suggestions. Finally, I want to thank my

editor Judy Bass for her enthusiasm and support.

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