P. BASIC CONCEPTS OF ALGEBRA P.1 The Real Numbers and Their Properties P.2 Integer Exponents and Scientific Notation P.3 Polynomials P.4 Factoring Polynomials P.5 Rational Expressions P.6 Rational Exponents and Radicals Chapter P Review and Tests Review Exercises Practice Test 1. EQUATIONS AND INEQUALITIES 1.1 Linear Equations in One Variable 1.2 Applications of Linear Equations: Modeling 1.3 Quadratic Equations 1.4 Complex Numbers: Quadratic Equations with Complex Solutions 1.5 Solving Other Types of Equations 1.6 Inequalities 1.7 Equations and Inequalities Involving Absolute Value Chapter 1 Review and Tests Review Exercises Practice Test A Practice Test B 2. GRAPHS AND FUNCTIONS 2.1 The Coordinate Plane 2.2 Graphs of Equations 2.3 Lines 2.4 Functions 2.5 Properties of Functions 2.6 A Library of Functions 2.7 Transformations of Functions 2.8 Combining Functions; Composite Functions 2.9 Inverse Functions Chapter 2 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P–2 3. POLYNOMIAL AND RATIONAL FUNCTIONS 3.1 Quadratic Functions 3.2 Polynomial Functions 3.3 Dividing Polynomials 3.4 The Real Zeros of a Polynomial Function 3.5 The Complex Zeros of a Polynomial Function 3.6 Rational Functions 3.7 Variation Chapter 3 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P–3 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS 4.1 Exponential Functions 4.2 Logarithmic Functions 4.3 Rules of Logarithms 4.4 Exponential and Logarithmic Equations and Inequalities 4.5 Logarithmic Scales; Modeling Chapter 4 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P–4 5. SYSTEMS OF EQUATIONS AND INEQUALITIES 5.1 Systems of Linear Equations in Two Variables 5.2 Systems of Linear Equations in Three Variables 5.3 Partial-Fraction Decomposition 5.4 Systems of Nonlinear Equations 5.5 Systems of Inequalities 5.6 Linear Programming Chapter 5 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P–5 6. MATRICES AND DETERMINANTS 6.1 Matrices and Systems of Equations 6.2 Matrix Algebra 6.3 The Matrix Inverse 6.4 Determinants and Cramer’s Rule Chapter 6 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P–6 7. CONIC SECTIONS 7.1 Conic Sections: Overview 7.2 The Parabola 7.3 The Ellipse 7.4 The Hyperbola Chapter 7 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P–7 8. FURTHER TOPICS IN ALGEBRA 8.1 Sequences and Series 8.2 Arithmetic Sequences; Partial Sums 8.3 Geometric Sequences and Series 8.4 Mathematical Induction 8.5 The Binomial Theorem 8.6 Counting Principles 8.7 Probability Chapter 8 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P–8 Answers to Selected Exercises Credits Index

About the Book Chapter openers: Each chapter opener includes a description of applications (one of them illustrated) relevant to the content of the chapter and the list of topics that will be covered. In one page, students see what they are going to learn and why they are learning it. Section opener with application:  Each section opens with a list of prerequisite topics, complete with section and page references, which students can review prior to starting the section. The Objectives of the section are also clearly stated and numbered, and then referenced again in the margin of the lesson at the point where the objective’s topic is taught. An Application then follows, containing  a  motivating  anecdote  or  an interesting problem. An example later in the section relating to this application and identified by the same icon is then solved using the mathematics covered in the section. These applications utilize material from a variety of fields: the physical and biological sciences (including health sciences), economics, art and architecture, history, and more. Definitions, Theorems, Properties, and Rules are all boxed and titled for emphasis and ease of reference. Work it out: Ratti/McWaters/Skryzpek encourage students to practice the material frequently, and give them ample opportunities to master the material by solving problems and applying their understanding. Procedure in Action is a special feature which introduces procedure steps within the context of a worked-out example. Important multistep procedures, such as the steps for finding the inverse of a one-to-one function, are presented in a two-column format. Examples include a wide range of computational, conceptual, and modern applied problems carefully selected to build confidence, competency, and understanding. Every example has a title indicating its purpose and presents a detailed solution containing annotated steps. All examples are followed by a Practice Problem for students to try so that they can check their understanding of the concept covered. UPDATED! Over 20% of exercises are updated, and over 500 brand-new exercises have been added.  New exercises primarily consist of applications that connect with students everyday experiences and enhance students conceptual understanding of graphing. REVISED! An improved balance of exercises provides a smoother transition from the less-challenging to the more-challenging exercises. Well-crafted Exercises are offered in a quantity, quality, and variety that meets the needs of all students. They are clearly labeled for instructors and students understanding of exercise expectations. The Basics NEW! Concepts and Vocabulary exercises begin each exercise set with problems that assess the student’s grasp of the definitions and ideas introduced in that section. These true/false and fill-in-the-blank exercises help to rapidly identify gaps in comprehension of the material in that section. Building Skills exercises develop fundamental skills; each odd-numbered exercise is closely paired with its consecutive even-numbered exercise. Applications Applying the Concepts features use the section’s material to solve real-world problems; all are titled and relevant to the topics of the section. Extensions Beyond the Basics exercises provide more challenging problems that give students an opportunity to reach beyond the material covered in the section; these are generally more theoretical in nature and are suitable for honors students, special assignments, or extra credit. NEW! Graph and Data-Related Exercises. These demonstrate how to extract information about real-world situations from a graphical representation of that situation, as well as how to recover algebraic or trigonometric formulations of a graph by using key characteristics of that graph. Critical Thinking/Discussion/Writing exercises, placed appropriately, are designed to develop students’ higher-level thinking skills. Calculator problems, identified by an icon, are included where needed. NEW! Getting Ready for the Next Section exercises end each exercise set with problems that provide a review of concepts and skills that will be used in the following section. NEW! Modeling Exercises. A section on building linear, exponential, logarithmic, and power models from data in Chapter 4 contains new exercises using each type of model. Help along the way: These integrated study aids give students hints and tips at strategic places in the text, addressing some of the most frequent issues and questions that occur in office hours. Summary of Main Facts boxes summarize information related to equations and their graphs, such as those of the conic sections. Side Notes provide hints for handling newly introduced concepts. Recall notes remind students of a key idea learned earlier in the text that will help them work through a current problem. Warnings appear as appropriate throughout the text to apprise students of common errors and pitfalls that can trip them up in their thinking or calculations. Technology Connections give students tips on using calculators to solve problems, check answers, and reinforce concepts. Note that the use of graphing calculators is optional in this text. Do You Know? features provide students with additional interesting information on topics to keep them engaged in the mathematics presented. Historical Notes give students information on key people or ideas in the history and development of mathematics. Preparation and review: End-of-chapter material includes all of the following items to help students prepare for exams and make the most of their study time.   An Updated Summary starts the end-of-chapter material, featuring an extensive review of the definitions, concepts, and formulas covered in that chapter with corresponding examples. This Review provides a description and examples of key topics indicating where the material occurs in the text, and encourages students to reread sections rather than memorize definitions out of context. Review Exercises provide students with an opportunity to practice what they have learned in the chapter. Two full Practice Tests–Practice Test A in the usual open-ended format and Practice Test B, covering the same topics, in a multiple-choice format. Cumulative Review Exercises appear at the end of every chapter, starting with Chapter 2, to remind students that mathematics is not modular and that what is learned in the first part of the book will be useful in later parts of the book and on the final examination. Check out the  preface for a complete list of features and what's new in this edition.  Also available with MyLab Math. MyLab™ Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Learn more about MyLab Math. NEW! MyLab Math Question Types enable students to develop and gauge their conceptual understanding. NEW! Concept and Vocabulary exercises start each section by assessing the student’s grasp of the definitions and ideas introduced in that section. These true/false and fill-in-the-blank exercises help to rapidly identify gaps in comprehension of the material in that section and are assignable in Pearson MyLab Math and Learning Catalytics. Video Assessment questions are assignable MyLab Math exercises tied to Example Solutions videos.  The questions are designed to check students’ understanding of the important math concepts covered in the video.  The videos and Video Assessment questions provide an active learning environment where students can work at their own pace. NEW! The Video Notebook is a guide that gives students a structured place to take notes and work on the example problems as they watch the Example Solution videos.  Definitions, examples, and important concepts are highlighted, and helpful hints are pointed out along the way.  The notebook is available in MyLab Math for download. NEW! Set Up & Solve exercises require students to show the setup of the solution for a particular exercise as well as the solution, helping them develop an overall problem-solving strategy before attempting the solution. NEW! Exercises preparing students for material in the next section–Each exercise section ends with a set of exercises that provide a review of concepts and skills that will be used in the following section. NEW! Enhanced Sample Assignments make course set-up easier by giving instructors a starting point for each section. Each assignment, handpicked by the authors to align with this text, includes a thoughtful mix of question types (e.g., conceptual, skills, etc.) specific to that topic. Personalized support and targeted practice to help all students succeed NEW! Skill Builder offers adaptive practice that is designed to increase students’ ability to complete their assignments. By monitoring student performance on their homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives. Getting Ready material provides just-in-time review, integrated throughout the course as needed to prepare students with prerequisite material to succeed.  From a quick quiz, a personalized, just-in-time review assignment is generated for each student, allowing them to refresh forgotten concepts. Visualization skills that deepen students’ understanding of the concepts Guided Visualizations enable users to interact with and manipulate figures to bring hard-to-convey math concepts to life. These are assignable in MyLab Math, integrated into the eText, and available to show in-class with accompanying as Exploratory Exercises in the Multimedia Library. Easier course set-up for instructors Enhanced Sample Assignments make course set-up easier by giving instructors a starting point for each chapter. Each assignment, handpicked by the author, includes a thoughtful mix of question types (e.g., conceptual, skills, etc.) specific to that topic.   The included video assessment questions can also be used alongside the Video Notebook with Worksheets. Student engagement and peer-to-peer learning NEW! Learning Catalytics™ helps instructors generate class discussion, customize lectures, and promote peer-to-peer learning with real-time analytics. As a student response tool, Learning Catalytics uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking. Upload a full PowerPoint® deck for easy creation of slide questions. Help your students develop critical thinking skills. Monitor responses to find out where your students are struggling. Rely on real-time data to adjust your teaching strategy. Automatically group students for discussion, teamwork, and peer-to-peer learning.

About the Book: Over 20% of exercises are updated, and a substantial amount of brand-new exercises have been added. An improved balance of exercises provides a smoother transition from the less-challenging to the more-challenging exercises. Well-crafted Exercises are offered in a quantity, quality, and variety that meets the needs of all students. They are clearly labeled for instructors and students understanding of exercise expectations. Getting Ready for the Next Section exercises end each exercise set with problems that provide a review of concepts and skills that will be used in the following section. Graph and Data-Related exercises—We have introduced exercises throughout the text that demonstrate how to extract information about real-world situations from a graphical representation of that situation, as well as how to recover algebraic or trigonometric formulations of a graph by using key characteristics of that graph. Modeling Exercises—A section on building linear, exponential, logarithmic, and power models from data was added in Chapter 4 that contains new exercises using each type of model. Concepts and Vocabulary exercises begin each exercise set with problems that assess the student’s grasp of the definitions and ideas introduced in that section. These true/false and fill-in-the-blank exercises help to rapidly identify gaps in comprehension of the material in that section. Exercises preparing students for material in the next section—Each exercise section ends with a set of exercises titled Getting Ready for the Next Section that provides a review of the concepts and skills that will be used in the following section. Content Changes: Chapter 1 Added a separate section Applications of Linear Equations Modeling as Section 1.2. This moved some material from Section 1.1 on linear equations into Section 1.2, providing two relatively short sections that are more easily covered. Introduced the discriminant, showing how to determine the number and type (rational or irrational) of solutions to a quadratic equation having integer coefficients. Provided simpler introductory examples for material students typically find especially difficult. Chapter 2 Introduced “delta x” and “delta y” notation when we discussed the slope of a line. Expanded the discussion on modeling data using linear regression. Added real-world examples to the discussion of increasing and decreasing functions and finding maxima and minima and expanded the discussion on turning points. Added real-world examples to the discussion of average rate of change. Chapter 3 A Summary of Main Facts has been added to the section on Quadratic Functions. Expanded the discussion on functions of even and odd degree and on the end behavior of polynomial functions. Added an example showing how to graph a polynomial given in factored form. Expanded the discussion on horizontal asymptotes along with improved graphics. Chapter 4 Added a schematic showing various transformations of the graph of f(x) = ax Expanded the discussion of Exponential Growth and Decay. Added a schematic showing various transformations of the graph of f(x) = logax Added a comparison of the end behavior (as x approaches infinity) of the exponential, logarithmic and linear functions. Added a procedure for solving logarithmic equations using exponential forms. Added material on building linear, exponential, logarithmic, and power models from data. Chapter 5 Added a summary of the methods for solving three equations in three unknowns. Added an example showing how to find a Partial-Fraction Decomposition when the denominator has repeated linear factors. Chapter 6 Added a schematic showing the most common transformations and their corresponding matrices. Added a discussion about the connection between combining transformations and multiplying their corresponding matrices and showing that the order in which the transformations are performed matters. Chapter 7 Sections 10.2, 10.3, and 10.4 each have additional examples showing how to obtain the equation of the conic discussed in that section from key characteristics of its graph. Chapter 8 Expanded discussion, with examples, showing the connection between arithmetic sequences and linear functions and between geometric sequences and exponential functions. Check out the  preface for a complete list of features and what's new in this edition.  Also available with MyLab Math MyLab™ Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Learn more about MyLab Math. Skill Builder offers adaptive practice that is designed to increase students’ ability to complete their assignments. By monitoring student performance on their homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives. Enhanced Sample Assignments make course set-up easier by giving instructors a starting point for each chapter. Each assignment, handpicked by the authors, includes a thoughtful mix of question types (e.g., conceptual, skills, etc.) specific to that topic.    MyLab Math Question Types enable students to develop and gauge their conceptual understanding. Concept and Vocabulary exercises start each section by assessing the student’s grasp of the definitions and ideas introduced in that section. These true/false and fill-in-the-blank exercises help to rapidly identify gaps in comprehension of the material in that section and are assignable in Pearson MyLab Math and Learning Catalytics. Video Assessment questions are assignable MyLab Math exercises tied to Example Solutions videos.  The questions are designed to check students’ understanding of the important math concepts covered in the video.  The videos and Video Assessment questions provide an active learning environment where students can work at their own pace. The Video Notebook is a guide that gives students a structured place to take notes and work on the example problems as they watch the Example Solution videos.  Definitions, examples, and important concepts are highlighted, and helpful hints are pointed out along the way.  The notebook is available in MyLab Math for download. Set Up & Solve exercises require students to show the setup of the solution for a particular exercise as well as the solution, helping them develop an overall problem-solving strategy before attempting the solution Exercises preparing students for material in the next section—Each exercise section ends with a set of exercises that provide a review of concepts and skills that will be used in the following section. Learning Catalytics™ helps instructors generate class discussion, customize lectures, and promote peer-to-peer learning with real-time analytics. As a student response tool, Learning Catalytics uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking. Upload a full PowerPoint® deck for easy creation of slide questions. Help your students develop critical-thinking skills. Monitor responses to find out where your students are struggling. Rely on real-time data to adjust your teaching strategy. Automatically group students for discussion, teamwork, and peer-to-peer learning.