xviii PREFACE 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 OF THIS TEXT 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.
RkJQdWJsaXNoZXIy NjM5ODQ=