# Graphical Approach to Algebra & Trigonometry, A, 7th edition

Published by Pearson (January 9, 2018) © 2019

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

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## MyLab

- Reach every student with personalized support
- Customize courses with ease
- Optimize learning with dynamic study tools

For courses in Algebra and Trigonometry.

### See, solve, apply

**A Graphical Approach to Algebra & Trigonometry, 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 Calculator****and 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. 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. Trigonometric Functions and Applications

- 9.1 Angles, Arcs, and Their Measures
- 9.2 Trigonometric Functions and Fundamental Identities
- 9.3 Right Triangles and Evaluating Trigonometric Functions
- 9.4 Applications of Right Triangles
- 9.5 The Circular Functions
- 9.6 Graphs of the Sine and Cosine Functions
- 9.7 Graphs of the Other Circular Functions
- 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

### 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
- 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 (Note: In the AIE, Instructor's Answers replaces Answers to Selected Exercises.)

#### Index

### 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.

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