When Julie Miller began writing her successful developmental math series, one of her primary goals was to bridge the gap between preparatory courses and college algebra. For thousands of students, the Miller/O'Neill/Hyde (or M/O/H) series has provided a solid foundation in developmental mathematics. With the Miller College Algebra series, Julie has carried forward her clear, concise writing style; highly effective pedagogical features; and complete author-created technological package to students in this course area. The main objectives of the college algebra series are three-fold:-Provide students with a clear and logical presentation of -the basic concepts that will prepare them for continued study in mathematics.-Help students develop logical thinking and problem-solving skills that will benefit them in all aspects of life.-Motivate students by demonstrating the significance of mathematics in their lives through practical applications.

Index of Applications xix

CHAPTER R Review of Prerequisites 1

Section R.1 Sets and the Real Number Line 2

Section R.2 Models, Algebraic Expressions, and Properties of Real Numbers 17

Section R.3 Integer Exponents and Scientific Notation 27

Section R.4 Rational Exponents and Radicals 39

Section R.5 Polynomials and Multiplication of Radicals 53

Problem Recognition Exercises Simplifying Algebraic Expressions 64

Section R.6 Factoring 65

Section R.7 Rational Expressions and More Operations on Radicals 76

Key Concepts 92

Review Exercises 94

Test 97

CHAPTER 1 Equations and Inequalities 99

Section 1.1 Linear Equations and Rational Equations 100

Section 1.2 Applications and Modeling with Linear Equations 113

Section 1.3 Complex Numbers 125

Section 1.4 Quadratic Equations 135

Problem Recognition Exercises Simplifying Expressions Versus

Solving Equations 148

Section 1.5 Applications of Quadratic Equations 148

Section 1.6 More Equations and Applications 158

Section 1.7 Linear Inequalities and Compound Inequalities 169

Section 1.8 Absolute Value Equations and Inequalities 179

Problem Recognition Exercises Recognizing and Solving Equations and Inequalities 187

Key Concepts 188

Review Exercises 190

Test 193

Cumulative Review Exercises 194

CHAPTER 2 Functions and Graphs 195

Section 2.1 The Rectangular Coordinate System and Graphing Utilities 196

Section 2.2 Circles 208

Section 2.3 Functions and Relations 214

Section 2.4 Linear Equations in Two Variables and Linear Functions 228

Section 2.5 Applications of Linear Equations and Modeling 244

Problem Recognition Exercises Comparing Graphs of Equations 261

Section 2 .6 Transformations of Graphs 262

Section 2.7 Analyzing Graphs of Functions and Piecewise-Defined Functions 275

Section 2.8 Algebra of Functions and Function Composit ion 295

Key Concepts 308

Review Exercises 31 O

Test 315

Cumulative Review Exercises 317

CHAPTER 3 Polynomial and Rational Functions 319

Section 3.1 Quadratic Functions and Applications 320

Section 3.2 Introduction to Polynomial Functions 333

Section 3.3 Division of Polynomials and the Remainder and Factor Theorems 348

Section 3.4 Zeros of Polynomials 361

Section 3.5 Rational Functions 377

Problem Recognition Exercises Polynomial and Rational Functions 398-399

Section 3.6 Polynomial and Rational Inequalities 399

Problem Recognition Exercises Solving Equations and Inequalities 412

Section 3.7 Variation 413

Key Concepts 421

Review Exercises 424

Test 427

Cumulative Review Exercises 429

CHAPTER 4 Exponential and Logarithmic Functions 431

Section 4.1 Inverse Functions 432

Section 4.2 Exponential Functions 444

Section 4 .3 Logarithmic Functions 458

Problem Recognition Exercises Analyzing Functions 473

Section 4.4 Properties of Logarithms 474

Section 4.5 Exponential and Logarithmic Equations 483

Section 4.6 Modeling with Exponential and Logarithmic Functions 497

Key Concepts 513

Review Exercises 515

Test 518

Cumulative Review Exercises 519

CHAPTER 5 Systems of Equations and Inequalities 521

Section 5.1 Systems of Linear Equations in Two Variables and Applications 522

Section 5.2 Systems of Linear Equations in Three Variables and Applications 535

Section 5.3 Partial Fraction Decomposition 546

Section 5.4 Systems of Nonlinear Equations in Two Variables 556

Section 5.5 Inequalities and Systems of Inequalities in Two Variables 565

Problem Recognition Exercises Equations and Inequalities in Two Variables 576

Section 5.6 Linear Programming 577

Key Concepts 586

Review Exercises 588

Test 590

Cumulative Review Exercises 591

Appendix A Additional Topics Appendix A-1 (Online only)

Student Answer Appendix SA-1

Credits C-1

Index 1-1

Donna Gerken i currently a professor at Miami Dade College where he has taught developmentalcour es, honors cla es, and upper-level mathematic cla es for 30 years. ThroughoUlthe years, she has been involved with ma ny projects at Miami Dade on curriculumredesign and the use of technology in the classroom. Donna·s bachelor of science inmathematics and master of c ience in mathematics are both from the Univer ity ofMiam i. Before fini shing her undergraduate a nd graduate degrees at the Univer ity ofMiami, she a lso attended Miami Dade College a a tudent where he discovered anamazing group of faculty who inspired her to continue on with a career in mathematic .Donna has kept a quote for many year that wa pa sed along from one of herundergraduate professors:Pure mathematics is, in irs way, rhe poerry of logical ideas.

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