# Graphical Approach to Precalculus with Limits, A,7th edition

• John Hornsby University of New Orleans
• Margaret L. Lial American River College
• Gary K. Rockswold Minnesota State University, Mankato

## eTextbook

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## MyLab

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For courses in Precalculus.

### See, solve, apply

A Graphical Approach to Precalculus with Limits, 7th Edition covers functions through a consistent 4-part process: 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 fosters a deep visual and graphical understanding of math, solidifying a stronger connection to the mathematical world. Careful chapter layouts, exercises, review questions and chapter features give students a comprehensive roadmap for success in the course.

### 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.

### 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.

### Features of MyLab Math for the 7th Edition

• Completely revamped MyLab Math video program:
• Unifying the Function videos were created by contributor Jessica Rockswold to spotlight the 4-step analytic process applied to each graph type: Analyzing the Graph, Solving an Equation, Solving an Inequality, and Solving an Application.
• Example Solution videos: 270 brand new videos, assignable in MyLab Math, are available to support students outside of the classroom and cover key topics in the text.  All section lecture videos have been replaced with up-to-date Example Solution videos for key topics for the 7th Edition. Lightboard technology creates a personal experience and simulates an in-class environment. MyLab Math video assessment exercises check conceptual understanding of the mathematics.
• GeoGebra Graphing Calculatorand Tutorials: Students can now launch GeoGebra's online graphing calculator from within their MyLab Math course. The GeoGebra icon next to relevant examples in the eText launches a pop-up version.
• Users can also download the free app to use while completing assignments. Interactive, self-checking tutorials make it easy to get started with this dynamic tool. All resources are available within the Graphing Resources tab in MyLab Math.
• New Question types in MyLab Math include drag & drop, video assessment exercises, Guided Visualization questions, plus Setup and Solve that require a higher level of decision making.
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
• 3.1 Complex Numbers
• 3.2 Quadratic Functions and Graphs
• Reviewing Basic Concepts (Sections 3.1 - 3.2)
• 3.3 Quadratic Equations and Inequalities
• 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– - .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 12.1 - 12.3)
• 12.4 Counting Theory
• 12.5 The Binomial Theorem
• Reviewing Basic Concepts (Sections 12.4 - 12.5)
• 12.6 Mathematical Induction
• 12.7 Probability
• Reviewing Basic Concepts (Sections 12.6 - 12.7)
• 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
• R. 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
• Test

### Appendices

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