We continue to improve the balance of exercises, providing a smoother transition from the less challenging to the more challenging exercises.

• Added a separate section, Applications of Linear Equations: Modeling, as Section 1.2. This moved some material from Section 1.1 on linear equations in the previous edition into Section 1.2, providing two relatively short sections that are more easily covered in one lecture.

• Introduced the discriminant, showing how to determine the number and type of solutions (rational or irrational) to a quadratic equation having integer coefficients.

• Provided simpler introductory examples for material students typically find difficult.

• 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.

• 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.

• Added a schematic showing various transformations of the graph of $f(x)=e^x\text{.}$

• Expanded the discussion of exponential growth and decay.

• Added a schematic showing various transformations of the graph of $f(x)={\log }_{a}x\text{.}$

• 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 form.

• Added material on building linear, exponential, logarithmic, and power models from data.

• 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.

• 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.

• Sections 7.2, 7.3, and 7.4 have additional examples showing how to obtain the equation of the conic discussed in that section from key characteristics of its graph.

• Expanded discussion, with examples, showing the connection between arithmetic sequences and linear functions and between geometric sequences and exponential functions.

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.

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 containing a motivating anecdote or an interesting problem then follows. 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.

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. Answers to the Practice Problems are provided just before the section exercises.

These boxes, interspersed throughout the text, present important procedures in numbered steps. Special Procedure in Action boxes present important multistep procedures, such as the steps for doing synthetic division, in a two-column format. The steps of the procedure are given in the left column, and an example is worked, following these steps, in the right column. This approach provides students with a clear model with which they can compare when encountering difficulty in their work. These boxes are a part of the numbered examples.

Definitions, Theorems, Properties, and Rules are all boxed and titled for emphasis and ease of reference.

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.

Summary of Main Facts boxes summarize information related to equations and their graphs, such as those of the conic sections.

A Calculus Symbol appears next to information in the text that is essential for the study of calculus.

• 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.

• 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.

The heart of any textbook is its exercises, so we have tried to ensure that the quantity, quality, and variety of exercises meet the needs of all students. Exercises are carefully graded to strengthen the skills developed in the section and are organized using the following categories. 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. 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. 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. Critical Thinking/Discussion/Writing exercises, appearing as appropriate, are designed to develop students’ higher-level thinking skills. Calculator problems, identified by , are included where needed. 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.

The chapter-ending material begins with an extensive Review featuring a two-column, section-by-section summary 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. Then students are given two chapter test options. They can take Practice Test A in the usual open-ended format and/or Practice Test B, covering the same topics, in a multiple-choice format. All tests are designed to increase student comprehension and verify that students have mastered the skills and concepts in the chapter. Mastery of these materials should indicate a true comprehension of the chapter and the likelihood of success on the associated in-class examination. 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.