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

  • Margaret L. Lial, 
  • John Hornsby, 
  • Gary K. Rockswold

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Overview

A Graphical Approach to Algebra & Trigonometry covers functions through a consistent, four-part analytical process to help you gain an understanding of math and make a stronger connection to the mathematical world around you.

Published by Pearson (December 11th 2020) - Copyright © 2019

ISBN-13: 9780137399925

Subject: Precalculus, College Algebra & Trigonometry

Category: Algebra & Trigonometry

Table of contents

Table of Contents

  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 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
  1. 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

Appendix A: Geometry Formulas

Appendix B: Vectors in Space

Appendix C: Polar Form of Conic Sections

Appendix D: Rotation of Axes

Instructor’s Answers

Answers to Selected Exercises*

Index

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

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