# College Algebra, 3rd Edition

# College Algebra, 3rd Edition

ISBN: 978-1-118-54311-5

Sep 2012

976 pages

## Description

The 3^{rd} edition of Cynthia Young's ** College Algebra** brings together all the elements that have allowed instructors and learners to successfully "bridge the gap" between classroom instruction and independent homework by overcoming common learning barriers and building confidence in students' ability to do mathematics. Written in a clear, voice that speaks to students and mirrors how instructors communicate in lecture, Young's hallmark pedagogy enables students to become independent, successful learners.

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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

**New Applications Added:**Applications to Economics, Business, Environmental Science, and Health have been added to each chapter to augment existing applications on Finance, Biology, and Chemistry.**Inquiry-Based Learning Projects added to every chapter!**These projects actively involve students in the learning process, aiding in understanding and mastery of the material.**Revised and Enriched Exercise Sets Throughout****Updated “Technology Tips”:**Optional technology tips in the margin demonstrate how students can use technology to confirm analytic solutions.**Chapter Revisions:**Section 1.4 now includes additional material and new exercises covering radical equations. New material has been added to Section 2.3 on Lines.**NEW Section 2.5 covering Least-square Linear Regression.**

**Clear, Concise and Inviting Writing.**The author's engaging and clear presentation is presented in a layout that is designed to reduce math anxiety in students.**Author Lecture Videos.**For review at home or for a class missed, Cynthia Young has recorded 244 instructional videos including worked examples and "Your Turn" problems from the text. These videos can be found in Wiley*PLUS*and are denoted in the text with an icon., accompanied with*WileyPLUS***Young,**, provides a research based, online environment for effective teaching and learning.*College Algebra 3*^{rd}edition*WileyPLUS*builds students’ confidence because it takes the guesswork out of studying by providing students with a clear roadmap: what to do, how to do it, if they did it right.**Six Different Types of Exercises.**Every chapter has skill, application, catch the mistake, challenge, conceptual, and technology exercises. The exercises gradually increase in difficulty and vary skill and conceptual emphasis.**Correct vs. Incorrect.**In addition to standard examples, some problems are worked both correctly and incorrectly to highlight common errors students make. Counter examples, like these, are often an effective learning approach for many students.**Catch the Mistake.**In every section, Catch the Mistake' exercises put the students in the role of the instructor grading homework which increases the depth of understanding and reinforces what they have learned.**Your Turn.**Students are often asked to work a problem immediately following an example to reinforce and check their understanding. This helps them build confidence as they progress in the chapter. These are ideal for in-class activity and preparing the student to work homework later.**Parallel Words and Math.**This text reverses the common presentation of examples by placing the explanation in words*on the left*and the mathematics in parallel*on the right*. This makes it easier for students to read through examples as the material flows more naturally and as commonly presented in lecture.**Modeling Our World.**Found in every chapter, these projects engage students by using real world data to model mathematical applications found in everyday life.**Chapter Cumulative Test.**Included at the end of each chapter to assess and improve students' retention of material.