Description

Book Synopsis


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. 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
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.

Graphical Approach to Precalculus with Limits A

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A Hardback by John Hornsby, Margaret Lial, Gary Rockswold

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    View other formats and editions of Graphical Approach to Precalculus with Limits A by John Hornsby

    Publisher: Pearson Education
    Publication Date: 1/9/2018 12:00:00 AM
    ISBN13: 9780134696492, 978-0134696492
    ISBN10: 0134696492
    Also in:
    Mathematics Calculus and mathematical analysis

    Description

    Book Synopsis


    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. 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
    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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