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

Published by Pearson (December 11, 2020) © 2019

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

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ISBN-13: 9780137399925
Graphical Approach to Algebra & Trigonometry, A
Published 2020

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A Graphical Approach to Algebra & Trigonometry covers functions through a consistent, 4-part process. The authors ask you 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 fosters a deep visual and graphical understanding of math, solidifying a stronger connection to the mathematical world around us. Careful chapter layouts, exercises, review questions and chapter features give you a comprehensive roadmap for success in the course. The 7th Edition adds a new Unifying the Function feature after introducing each major class of functions; updates data throughout with new topics including active Twitter users, organic food sales and more; adds nearly 500 new or updated exercises; and much more.

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

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