Title Details

0 Prerequisites and Review 2

0.1 Real Numbers 4

0.2 Integer Exponents and Scientific Notation 18

0.3 Polynomials: Basic Operations 28

0.4 Factoring Polynomials 37

0.5 Rational Expressions 48

0.6 Rational Exponents and Radicals 63

0.7 Complex Numbers 73

Inquiry-Based Learning Project 81

Review 83

Review Exercises 86

Practice Test 88

1 Equations and Inequalities 90

1.1 Linear Equations 92

1.2 Applications Involving Linear Equations 102

1.3 Quadratic Equations 116

1.4 Other Types of Equations 130

1.5 Linear Inequalities 140

1.6 Polynomial and Rational Inequalities 151

1.7 Absolute Value Equations and Inequalities 162

Inquiry-Based Learning Project 170

Modeling Our World 172

Review 173

Review Exercises 174

Practice Test 178

Cumulative Test 179

2 Graphs 180

2.1 Basic Tools: Cartesian Plane, Distance, and Midpoint 182

2.2 Graphing Equations: Point-Plotting, Intercepts, and Symmetry 190

2.3 Lines 204

2.4 Circles 221

2.5 Linear Regression: Best Fit 230

Inquiry-Based Learning Project 256

Modeling Our World 258

Review 260

Review Exercises 261

Practice Test 264

Cumulative Test 265

3 Functions and Their Graphs 266

3.1 Functions 268

3.2 Graphs of Functions; Piecewise-Defined Functions; Increasing and Decreasing Functions; Average Rate of Change 287

3.3 Graphing Techniques: Transformations 308

3.4 Operations on Functions and Composition of Functions 323
 
3.5 One-to-One Functions and Inverse Functions 334

3.6 Modeling Functions Using Variation 350

Inquiry-Based Learning Project 361

Modeling Our World 363

Review 364

Review Exercises 366

Practice Test 371

Cumulative Test 373

4 Polynomial and Rational Functions 374

4.1 Quadratic Functions 376

4.2 Polynomial Functions of Higher Degree 394

4.3 Dividing Polynomials: Long Division and Synthetic Division 410

4.4 The Real Zeros of a Polynomial Function 419

4.5 Complex Zeros: The Fundamental Theorem of Algebra 435

4.6 Rational Functions 445

Inquiry-Based Learning Project 466

Modeling Our World 467

Review 469

Review Exercises 472

Practice Test 476

Cumulative Test 477

5 Exponential and Logarithmic Functions 478

5.1 Exponential Functions and Their Graphs 480

5.2 Logarithmic Functions and Their Graphs 496

5.3 Properties of Logarithms 512

5.4 Exponential and Logarithmic Equations 521

5.5 Exponential and Logarithmic Models 532

Inquiry-Based Learning Project 544

Modeling Our World 545

Review 547

Review Exercises 549

Practice Test 552

Cumulative Test 553

6 Systems of Linear Equations and Inequalities 554

6.1 Systems of Linear Equations in Two Variables 556

6.2 Systems of Linear Equations in Three Variables 573

6.3 Partial Fractions 586

6.4 Systems of Linear Inequalities in Two Variables 598

6.5 The Linear Programming model 610

Inquiry-Based Learning Project 618

Modeling Our World 619

Review 621

Review Exercises 623

Practice Test 626

Cumulative Test 627

7 Matrices 628

7.1 Matrices and Systems of Linear Equations 630

7.2 Matrix Algebra 653

7.3 Matrix Equations; The Inverse of a Square Matrix 667

7.4 The Determinant of a Square Matrix and Cramers Rule 681
Inquiry-Based Learning Project 696

Modeling Our World 697

Review 699

Review Exercises 702

Practice Test 705

Cumulative Test 707

8 Conics and Systems of Nonlinear Equations and Inequalities 708

8.1 Conic Basics 710

8.2 The Parabola 713

8.3 The Ellipse 726

8.4 The Hyperbola 739

8.5 Systems of Nonlinear Equations 752

8.6 Systems of Nonlinear Inequalities 763

Inquiry-Based Learning Application 771

Modeling Our World 773

Review 774

Review Exercises 777

Practice Test 780

Cumulative Test 781

9 Sequences, Series, and Probability 782

9.1 Sequences and Series 784

9.2 Arithmetic Sequences and Series 795

9.3 Geometric Sequences and Series 804

9.4 Mathematical Induction 816

9.5 The Binomial Theorem 821

9.6 Counting, Permutations, and Combinations 829

9.7 Probability 839

Inquiry-Based Learning Project 849

Modeling Our World 851

Review 852

Review Exercises 854

Practice Test 858

Cumulative Test 859

Answers to Odd Numbered Exercises 860

Applications Index 929

Subject Index 933