College Algebra Pearson New International Edition
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R. Basic Concepts of Algebra
R.1 The Real-Number System
R.2 Integer Exponents, Scientific Notation, and Order of Operations
R.3 Addition, Subtraction, and Multiplication of Polynomials
R.4 Factoring
R.5 The Basics of Equation Solving
R.6 Rational Expressions
R.7 Radical Notation and Rational Exponents
Study Guide
Review Exercises
Chapter Test
1. Graphs; Linear Functions and Models
1.1 Introduction to Graphing
1.2 Functions and Graphs
1.3 Linear Functions, Slope, and Applications
Visualizing the Graph
Mid-Chapter Mixed Review
1.4 Equations of Lines and Modeling
1.5 Linear Equations, Functions, Zeros, and Applications
1.6 Solving Linear Inequalities
Study Guide
Review Exercises
Chapter Test
2. More on Functions
2.1 Increasing, Decreasing, and Piecewise Functions; Applications
2.2 The Algebra of Functions
2.3 The Composition of Functions
2.4 Symmetry and Transformations
Visualizing the Graph
2.5 Variation and Applications
Study Guide
Review Exercises
Chapter Test
3. Quadratic Functions and Equations; Inequalities
3.1 The Complex Numbers
3.2 Quadratic Equations, Functions, Zeros, and Models
3.3 Analyzing Graphs of Quadratic Functions
Visualizing the Graph
Mid-Chapter Mixed Review
3.4 Solving Rational Equations and Radical Equations
3.5 Solving Linear Inequalities
Study Guide
Review Exercises
Chapter Test
4. Polynomial and Rational Functions
4.1 Polynomial Functions and Modeling
4.2 Graphing Polynomial Functions
Visualizing the Graph
4.3 Polynomial Division; The Remainder and Factor Theorems
Mid-Chapter Mixed Review
4.4 Theorems about Zeros of Polynomial Functions
4.5 Rational Functions
Visualizing the Graph
4.6 Polynomial and Rational Inequalities
Study Guide
Review Exercises
Chapter Test
5. Exponential and Logarithmic Functions
5.1 Inverse Functions
5.2 Exponential Functions and Graphs
5.3 Logarithmic Functions and Graphs
5.4 Properties of Logarithmic Functions
5.5 Solving Exponential Equations and Logarithmic Equations
5.6 Applications and Models: Growth and Decay; Compound Interest
Study Guide
Review Exercises
Chapter Test
6. Systems of Equations and Matrices
6.1 Systems of Equations in Two Variables
Visualizing the Graph
6.2 Systems of Equations in Three Variables
6.3 Matrices and Systems of Equations
6.4 Matrix Operations
Mid-Chapter Mixed Review
6.5 Inverses of Matrices
6.6 Determinants and Cramer’s Rule
6.7 Systems of Inequalities and Linear Programming
6.8 Partial Fractions
Study Guide
Review Exercises
Chapter Test
7. Conic Sections
7.1 The Parabola
7.2 The Circle and the Ellipse
Mid-Chapter Mixed Review
7.3 The Hyperbola
7.4 Nonlinear Systems of Equations and Inequalities
Visualizing the Graph
Study Guide
Review Exercises
Chapter Test
Photo Credits
Answers
Index
Index of Applications
- Functions appear early and integrated, reflecting the authors’ belief that functions are best taught as a theme of the course, not as an isolated topic.
- Functions are introduced in Chapter 1, so that students to start the course with a new topic rather than a review of equation-solving that was covered in previous math courses.
- Students will come to understand the concept of a function by being exposed repeatedly to thelanguage, notation, and use of functions throughout the text.
- The authors take a visual approach to the course. The early introduction to functions allows for the use of graphs to provide a visual aspect to solving equations and inequalities. In addition, specific features enable students to “see the math” and make connections between concepts.
- Algebraic/Graphical Side-by-Side Examples present the solutions in a two-column format to help students understand the connection between algebraic manipulation and the graphical interpretation.
- Visualizing the Graph exercises help develop students’ ability to make the mental link between different types of equations and their corresponding graphs.
- Connecting the Concepts, a hallmark feature of the text, invites the student to stop and check their understanding of how concepts work together in one section or several sections. Concepts are summarized visually–using graphs, outlines, or charts–so that students deepen their understanding and make connections.
- Ongoing review features throughout the text reinforce the concepts and help students build understanding.
- NEW! Mid-chapter Review exercises are one-page mixed review sets at logical breaks in the chapter, helping students to reinforce their understanding of the concepts. These exercises are assignable in MyMathLab.
- NEW! Study Summaries have been added to the Chapter Review, giving students a built-in study aid when reviewing and preparing for tests. In MyMathLab, these Study Summaries are accompanied by new videos to reinforce the key concepts and ideas.
- Enhanced! Vocabulary Review exercises appear in the last section of each chapter, and check students’ understanding of the language of mathematics. These are now assignable in MyMathLab and can serve as reading quizzes.
- Enhanced! Synthesis exercises, included at the end of each exercise set, encourage critical thinking by asking students to apply multiple skills or concepts within a single exercise. For the Fourth Edition, these are assignable in MyMathLab.
- Classify the Function exercises, appearing in the Skill Maintenance section of the exercise sets, ask students to identify a number of functions by their type (linear, quadratic, rational, etc.). Throughout the text, the variety of functions increases and these exercises become more challenging.
- Review Icons refer students to an earlier, related section where they can go to review prerequisite concepts that are needed for the current section.
- Study Tips are occasional, brief reminders in the margin, to promote effective study habits such as good note taking and exam preparation.
- Technology Connections are optional sections that guide students in the use of the graphing calculator as another way to check problems.
- Zeros, Solutions, andx-Intercepts are a theme of the text. The authors aim to help students see the connection between the real zeros of the function, the solutions of the associated equation, and the first coordinates of the x-intercepts of the graph. When students develop their understanding of these connections, their probability of success increases for this course.
- Additional ongoing review features have been integrated throughout, to help students reinforce their understanding and improve their success in the course.
- Mid-chapter Review exercises are one-page mixed review sets at logical breaks in the chapter, helping students reinforce their understanding of the concepts.
- Study Summaries have been added to the Chapter Review, giving students a built-in study aid when reviewing and preparing for tests.
- MyMathLab is more closely integrated with the text and now offers new question types, for a more robust online experience that mirrors the authors’ approach.
- Example-based videos, created by the authors themselves, walk students through the detailed solution process for key examples in the textbook. Videos have optional subtitles.
- Vocabulary exercises have been added, which can serve as reading quizzes.
- Mid-chapter Reviews are new to the text and are assignable online, helping students to reinforce their understanding of the concepts.
- Synthesis exercises are now assignable online, testing students’ ability to answer questions that cover multiple concepts.
- Study Summaries are new to the text, and in MyMathLab theseare accompanied bysection summary videos, which cover key definition and procedures from the text.
- Sample homework assignments are pre-selected by the authors for each section. These are indicated in the Annotated Instructor Edition by a blue underline within each end-of-section exercise set. These homework sets are assignable in MyMathLab.
- The first four chapters of the text have been reorganized, to make the material easier to teach and learn. By presenting this material in four chapters rather than three, the level of difficulty is more balanced in this new edition.