Graphical Approach to Precalculus with Limits, A

Description

About our authors

When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics, education or journalism. His ultimate decision was to become a teacher, but after 25 years of teaching at the high school and university levels and 15 years of writing mathematics textbooks, all 3 of his goals have been realized; his love for teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history and incorporating graphing calculators into the curriculum. John’s personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John’s other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.

The late Marge Lial was always interested in math; it was her favorite subject in the first grade! Marge’s intense desire to educate both her students and herself inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor’s and Master’s degrees from California State University at Sacramento, was most recently affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. She was particularly interested in archeology, and trips to various digs and ruin sites produced fascinating problems for her textbooks, involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.

Gary Rockswold has been teaching mathematics for 33 years at all levels from seventh grade to graduate school, including junior high and high school students, talented youth, vocational, undergraduate and graduate students, and adult education classes. Now retired, he most recently served as professor of mathematics at Minnesota State University – Mankato. He graduated with majors in mathematics and physics from St. Olaf College in Northfield, Minnesota, where he was elected to Phi Beta Kappa. He received his Ph.D. in applied mathematics from Iowa State University. He has an interdisciplinary background and has also taught physical science, astronomy and computer science. Outside of mathematics, he enjoys spending time with his lovely wife and 2 children.

New and updated features of this title

• New Unifying the Function feature appears after the introduction of each of the major classes of functions.
  • It provides a concise summary of the 4-step analytic process that drives this text: Analyze the Graph, Solve an Equation, Solve an Inequality and Solve a Related Application.
  • Each instance of this new feature has a corresponding video and is assignable in MyLab Math with accompanying assessment questions.
• Chapter 3 from the previous edition is now split into 2 chapters at the suggestion of reviewers.
• Data has been updated throughout. Some new application topics include organic food sales, video-on-demand, active Twitter users, wearable technology, U.S. Snapchat users and online gaming revenue.
• Nearly 500 updated or new exercises have been added.

1. Linear Functions, Equations, and Inequalities
   • 1.1 Real Numbers and the Rectangular Coordinate System
   • 1.2 Introduction to Relations and Functions
     • Reviewing Basic Concepts (Sections 1.1–1.2)
   • 1.3 Linear Functions
   • 1.4 Equations of Lines and Linear Models
     • Reviewing Basic Concepts (Sections 1.3–1.4)
   • 1.5 Linear Equations and Inequalities
   • Unifying Linear Functions
   • 1.6 Applications of Linear Functions
     • Reviewing Basic Concepts (Sections 1.5–1.6)
   • Summary
   • Review Exercises
   • Test
2. Analysis of Graphs of Functions
   • 2.1 Graphs of Basic Functions and Relations; Symmetry
   • 2.2 Vertical and Horizontal Shifts of Graphs
   • 2.3 Stretching, Shrinking, and Reflecting Graphs
     • Reviewing Basic Concepts (Sections 2.1–2.3)
   • 2.4 Absolute Value Functions
     • Unifying Absolute Value Functions
   • 2.5 Piecewise-Defined Functions
   • 2.6 Operations and Composition
     • Reviewing Basic Concepts (Sections 2.4–2.6)
   • Summary
   • Review Exercises
   • Test
3. Quadratic Functions
   • 3.1 Complex Numbers
   • 3.2 Quadratic Functions and Graphs
     • Reviewing Basic Concepts (Sections 3.1–3.2)
   • 3.3 Quadratic Equations and Inequalities
     • Unifying Quadratic Functions
   • 3.4 Applications of Quadratic Functions and Models
     • Reviewing Basic Concepts (Sections 3.3–3.4)
   • Summary
   • Review Exercises
   • Test
4. Polynomial Functions of Higher Degree
   • 4.1 Graphs of Polynomial Functions
   • 4.2 Topics in the Theory of Polynomial Functions (I)
     • Reviewing Basic Concepts (Sections 4.1–4.2)
   • 4.3 Topics in the Theory of Polynomial Functions (II)
   • 4.4 Polynomial Equations, Inequalities, Applications, and Models
     • Reviewing Basic Concepts (Sections 4.3–4.4)
     • Unifying Polynomial Functions
   • Summary
   • Review Exercises
   • Test
5. Rational, Power, and Root Functions
   • 5.1 Rational Functions and Graphs (I)
   • 5.2 Rational Functions and Graphs (II)
   • 5.3 Rational Equations, Inequalities, Models, and Applications
     • Reviewing Basic Concepts (Sections 5.1–5.3)
   • 5.4 Functions Defined by Powers and Roots
   • 5.5 Equations, Inequalities, and Applications Involving Root Functions
     • Reviewing Basic Concepts (Sections 5.4–5.5)
     • Unifying Root Functions
   • Summary
   • Review Exercises
   • Test
6. Inverse, Exponential, and Logarithmic Functions
   • 6.1 Inverse Functions
   • 6.2 Exponential Functions
     • Unifying Exponential Functions
   • 6.3 Logarithms and Their Properties
     • Reviewing Basic Concepts (Sections 6.1¿–6.3)
   • 6.4 Logarithmic Functions
   • 6.5 Exponential and Logarithmic Equations and Inequalities
     • Unifying Logarithmic Functions
   • 6.6 Further Applications and Modeling with Exponential and Logarithmic Functions
     • Reviewing Basic Concepts (Sections 6.4–6.6)
     • Summary Exercises on Functions: Domains, Defining Equations, and Composition
   • Summary
   • Review Exercises
   • Test
7. Systems and Matrices
   • 7.1 Systems of Equations
   • 7.2 Solution of Linear Systems in Three Variables
   • 7.3 Solution of Linear Systems by Row Transformations
     • Reviewing Basic Concepts (Sections 7.1–7.3)
   • 7.4 Matrix Properties and Operations
   • 7.5 Determinants and Cramer’s Rule
   • 7.6 Solution of Linear Systems by Matrix Inverses
     • Reviewing Basic Concepts (Sections 7.4–7.6)
   • 7.7 Systems of Inequalities and Linear Programming
   • 7.8 Partial Fractions
     • Reviewing Basic Concepts (Sections 7.7–7.8)
   • Summary
   • Review Exercises
   • Test
8. Conic Sections, Nonlinear Systems, and Parametric Equations
   • 8.1 Circles Revisited and Parabolas
   • 8.2 Ellipses and Hyperbolas
     • Reviewing Basic Concepts (Sections 8.1–8.2)
   • 8.3 The Conic Sections and Nonlinear Systems
   • 8.4 Introduction to Parametric Equations
     • Reviewing Basic Concepts (Sections 8.3–8.4)
   • Summary
   • Review Exercises
   • Test
9. The Unit Circle and the Functions of Trigonometry
   • 9.1 Angles, Arcs, and Their Measures
   • 9.2 The Unit Circle and Its Functions
   • 9.3 Graphs of the Sine and Cosine Functions
   • 9.4 Graphs of the Other Circular Functions
   • 9.5 Functions of Angles and Fundamental Angles
   • 9.6 Evaluating Trigonometric Functions
   • 9.7 Applications of Right Triangles
   • 9.8 Harmonic Motion
   • Summary
   • Review Exercises
   • Test
10. Trigonometric Identities and Equations
    • 10.1 Trigonometric Identities
    • 10.2 Sum and Difference Identities
    • 10.3 Further Identities
    • 10.4 The Inverse Circular Functions
    • 10.5 Trigonometric Equations and Inequalities (I)
    • 10.6 Trigonometric Equations and Inequalities (II)
      • Unifying Trigonometric Functions
    • Summary
    • Review Exercises
    • Test
11. Applications of Trigonometry and Vectors
    • 11.1 The Law of Sines
    • 11.2 The Law of Cosines and Area Formulas
    • 11.3 Vectors and Their Applications
    • 11.4 Trigonometric (Polar) Form of Complex Numbers
    • 11.5 Powers and Roots of Complex Numbers
    • 11.6 Polar Equations and Graphs
    • 11.7 More Parametric Equations
    • Summary
    • Review Exercises
    • Test
12. Further Topics in Algebra
    • 12.1 Sequences and Series
    • 12.2 Arithmetic Sequences and Series
    • 12.3 Geometric Sequences and Series
      • Reviewing Basic Concepts (Sections 9.1–9.3)
    • 12.4 Counting Theory
    • 12.5 The Binomial Theorem
      • Reviewing Basic Concepts (Sections 9.4–9.5)
    • 12.6 Mathematical Induction
    • 12.7 Probability
      • Reviewing Basic Concepts (Sections 9.6–9.7)
    • Summary
    • Review Exercises
    • Test
13. Limits, Derivatives, and Definite Integrals
    • 13.1 An Introduction to Limits
    • 13.2 Techniques for Calculating Limits
    • 13.3 One-Sided Limits and Limits Involving Infinity
    • 13.4 Tangent Lines and Derivatives
    • 13.5 Area and the Definite Integral
14. Review: Basic Algebraic Concepts
    • R.1 Review of Sets
    • R.2 Review of Exponents and Polynomials
    • R.3 Review of Factoring
    • R.4 Review of Rational Expressions
    • R.5 Review of Negative and Rational Exponents
    • R.6 Review of Radicals
    • Test

Appendices

• A. Geometry Formulas
• B. Vectors in Space
• C. Polar Form of Conic Sections
• D. Rotation of Axes

Instructor’s Answers

Answers to Selected Exercises*

Index

• *In the AIE, Instructor’s Answers replaces Answers to Selected Exercises.

Hallmark features of this title

• Algebra Reviews refer students to finding additional help with important topics from algebra.
• Pointers include on-the-spot reminders and warnings about common pitfalls.
• Function Capsule boxes are a comprehensive, visual introduction to each class of function. Each includes traditional and calculator graphs and a calculator table of values, plus the domain, range and other specific information about the function.
• What Went Wrong? anticipates typical errors made when using graphing technology. Answers are included on the same page.
• Cautions and Notes warn of common errors and emphasize important ideas throughout.
• Looking Ahead to Calculus notes provide glimpses of how the algebraic topics being studied are used in calculus.

NOTE: This edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value; this format costs significantly less than a new textbook. Before purchasing, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. For Books a la Carte editions that include MyLab™ or Mastering™, several versions may exist for each title—including customized versions for individual schools—and registrations are not transferable. In addition, you may need a Course ID, provided by your instructor, to register for and use MyLab or Mastering platforms.

For courses in precalculus.

Unifies the theme of a function — See, Solve, Apply

The Graphical Approach series by Hornsby, Lial, and Rockswold covers functions through a consistent, four-part analytical process. The authors ask students to:

1: [See] Examine the nature of the graph

2: Solve a typical equation analytically and graphically

3: Solve the related inequality analytically and graphically

4: Apply analytic and graphical methods to solve an application.

This proven approach helps students gain a deep visual and graphical understanding of math, solidifying a stronger connection to the mathematical world around them. The authors also support analytical thinking with sound pedagogy; chapter layouts, exercises, review questions, and chapter features give students a comprehensive roadmap for success in the course.

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 personalizes the learning experience and improves results for each student. Learn more about MyLab Math.

NOTE: This edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value; this format costs significantly less than a new textbook. Before purchasing, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. For Books a la Carte editions that include MyLabTM or MasteringTM, several versions may exist for each title–including customized versions for individual schools–and registrations are not transferable. In addition, you may need a Course ID, provided by your instructor, to register for and use MyLab or Mastering platforms.

For courses in precalculus.

Unifies the theme of a function – See, Solve, Apply

The Graphical Approach series by Hornsby, Lial, and Rockswold covers functions through a consistent, four-part analytical process. The authors ask students to:

1: [See] Examine the nature of the graph

2: Solve a typical equation analytically and graphically

3: Solve the related inequality analytically and graphically

4: Apply analytic and graphical methods to solve an application

This proven approach helps students gain a deep visual and graphical understanding of math, solidifying a stronger connection to the mathematical world around them.

Also available with MyLab Math

MyLabTM Math is the teaching and learning platform that empowers instructors to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student.

Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.

If you would like to purchase both the physical text and MyLab Math, search for:

013486221X / 9780134862217 A Graphical Approach to Precalculus with Limits, Books a la Carte Edition Plus MyLab Math with Pearson eText — Access Card Package, 7/e Package consists of:

• 0134698223 / 9780134698229 A Graphical Approach to Precalculus with Limits, Books a la Carte Edition
• 0134859170 / 9780134859170 MyLab Math with Pearson eText – Standalone Access Card – for A Graphical Approach to Precalculus with Limits

Additional information

Dimensions	1.75 × 8.60 × 11.20 in
Imprint	Pearson
Format	gen
ISBN-13	09780134698229
ISBN-10	0134698223
Author	John Hornsby, Margaret L. Lial, Gary K. Rockswold
BISAC	MAT023000
Subjects	mathematics, higher education, MAT023000, Precalculus