College Algebra and Trigonometry [RENTAL EDITION] (7th Edition)

Book Preface

In the seventh edition of College Algebra and Trigonometry, we continue our ongoing commitment to providing the best possible text to help instructors teach and students succeed. In this edition. we have remained true lo the pedagogical style of the past while staying focused on the needs of today’s students. Support for all classroom types (traditional, corequisite, flipped, hybrid, and online) may be found in this classic text and its supplements backed by the power of Pearson’s MyLab Math.
Tn this edition, we have drawn on the extensive teaching experience of the Lial team, with special consideration given to reviewer suggestions. General updates include enhanced readability as we continually strive to make math understandable for students, updates to our extensive list of applications and real-world mathematics problems, use of color in displays and side comments, and coordination of exercises and their related examples.
The authors understand that teaching and learning mathematics today can be a challenging task. Some student? are prepared for the challenge, while other student? require more review and supplemental mate1ial. This text is w1itten so that students with varying abilities and backgrounds will all have an opportunity for a successful learning experience.
The Lial team believes this to be our best edition of College Algebra and Trigo­nometry yet, and we sincerely hope that you enjoy using it as much as we have enjoyed writing it. Additional textbooks in this series are

College Algebra, Thitieenth Edition Trigonometry, Twelfth Edition Precalculus, Seventh Edition.

HIGHLIGHTS OF NEW CONTENT

Chapter R has been expanded to include more of the basic concepts many students struggle with. It begins with new Section R.l Fractions, Decimals, and Percents. Additional new topics have been inserted throughout the chapter, including operations with signed numbers (Section R.3), divid­ing a polynomial by a monomial (Section R.5), and factoring expressions with negative and rational exponents (Section R.6). Topics throughout the chapter have been reorganized for improved flow.

Instructors may choose to cover review topics from Chapter R at the beginning of a course or to insert these topics as-needed in a just-in-time fashion. Either way, stlldents who are under-prepared for the demands of college algebra and trigonometry, as welJ as those who need a quick review, will benefit from the material contained here.

The exercise sets were a key focus of this revision, and Chapters 1 and 2 are among the chapters that have benefitted. Specifically, Section I. 7 Inequalities has new exercises on solving quadratic and rational inequali­ties, and Section 1.8 Absolute Value Equations and Inequalities con­tains new exercises that involve the absolute value of a quadratic polynomial. Section 2.3 }<‘unctions has new exercises that use analytic methods to determine maximum and minimum vaJues of a function.

Section 2.6 Graphs of Basic Functions contains new exercises and applications using the greatest integer function. Section 2.4 Linear Functions includes enhanced discussion of the average rate of change of a linear function. This topic is then related to the difference quotient and the average rate of change of a nonlinear function in Section 2.8 Function Operations and Composition.

■ Chapter 3 includes new Section 3.6 Polynomial and Rational Inequali­ties. This section features a visual approach to solving such inequalities by interpreting the graphs of related functions.
■ In response to reviewer suggestions, Section 4.3 Logarithmic Functions has new exercises that relate exponential and logarithmic functions as inverses. Chapter 6 includes additional exercises devoted to finding arc length and area of a sector of a circle (Section 6.1), as well as new applications of linear and angular speed (Section 6.2) and harmonic motion (Section 6.7).
■ Proofs of identities in Chapter 7 now feature a drop-down style for increased clarity and student understanding. Based on reviewer requests, Section 7.7 Equations Involving Inverse Trigonometric Functions includes new exer­cises in which solutions of inverse trigonometric equations are found.
■ .Based on reviewer feedback, Section 8.4 Algebraically Defined Vectors and the Dot Product has new exercises on finding the angle between two vectors, determining magnitude and direction angle for a vector, and identi­fying orthogonal vectors. Additionally, Chapter 8 contains new exercises requiring students to graph polar and parametric equations (Section 8. 7) and give parametric representations of plane curves (Section 8.8).
■ Section 9.2 Matrix Solution of Linear Systems now includes a new example and related exercises that use Gaussian elimination to solve lin­ear systems of equations. Section 10.2 Ellipses and Section 10.3 Hyperbolas include new examples and exercises in which completing the square is used to find the standard form of an ellipse or a hyperbola.

FEATURES OFTHISTEXT

SUPPORT FOR LEARNING CONCEPTS

We provide a variety of features to support students’ learning of the essential topics of college algebra and trigonometry. Explanations that are written in understandable terms, figures and graphs that illustrate examples and concepts, graphing technol­ogy that supports and enhances algebraic manipulations, and real-life applications that enrich the topics with meaning all provide opportunities for students to deepen their understanding of mathematics. These features help students make mathemati­cal connections and expand their own knowledge base.

■ Examples Numbered examples that illustrate the techniques for working exercises are found in every section. We use traditional explanations, side comments, and pointers to describe the steps taken-and to warn students about common pitfalls. Some examples provide additional graphing calcula­tor solutions, although these can be omitted if desired.

■ Now Try Exercises Following each numbered example, the student is directed to try a corresponding odd-numbered exercise (or exercises). This feature allows for quick feedback to determine whether the student understands the principles illustrated in the example.

■ Real-Life Applications We have included hundreds of real-life applica­tions, many with data updated from the previous edition. They come from fields such as business, entertainment, sports, biology, astronomy, geology, and environmental studies.

■ Function Boxes Beginning in Chapter 2, functions provide a unifying theme throughout the text. Special function boxes offer a comprehensive, visual introduction to each type of function and also serve as an excellent resource for reference and review. Each function box includes a table of vaJ­ues, traditional and calculator-generated graphs, the domain, the range, and other special information about the function. These boxes are assignable in MyLab Math.

■ Figures and Photos Today’s students are more visually oriented than ever before, and we have updated the figures and photos in this edition to promote visual appeal. Guided Visualizations with accompanying exercises and explorations are available and assignable in MyLab Math.

■ Cautions and Notes Text that is marked 1w1ji(11¢1 warns students of common errors, and NOTE comments point out explanations that should receive particular attention.

■ Looking Ahead to Calculus These margin notes offer glimpses of how the topics currently being studied are used in calculus.

■ Use of Graphing Technology We have integrated the use of graphing calculators where appropriate, although this technology is completely optional and can be omitted without loss of continuity. We contiuue to stress that graphing calculators suppmt understanding but that students must first master the underlying mathematical concepts. Exercises that require the use of a graphing calculator are marked with the icon?-