Precalculus, 11th edition

  • Michael Sullivan

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Overview

Precalculus uses a cycle of continuous preparation and retention, along with quality exercises, to reinforce what you know.

Published by Pearson (July 15th 2020) - Copyright © 2020

ISBN-13: 9780136872733

Subject: Precalculus, College Algebra & Trigonometry

Category: Precalculus

Table of contents

Table of Contents

  1. Graphs
    • 1.1 The Distance and Midpoint Formulas
    • 1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
    • 1.3 Lines
    • 1.4 Circles
    • Chapter 1 Review, Test, and Projects
  2. Functions and Their Graphs
    • 2.1 Functions
    • 2.2 The Graph of a Function
    • 2.3 Properties of Functions
    • 2.4 Library of Functions; Piecewise-defined Functions
    • 2.5 Graphing Techniques: Transformations
    • 2.6 Mathematical Models: Building Functions
    • Chapter 2 Review, Test, and Projects
  3. Linear and Quadratic Functions
    • 3.1 Properties of Linear Functions and Linear Models
    • 3.2 Building Linear Models from Data
    • 3.3 Quadratic Functions and Their Properties
    • 3.4 Build Quadratic Models from Verbal Descriptions and from Data
    • 3.5 Inequalities Involving Quadratic Functions
    • Chapter 3 Review, Test, and Projects
  4. Polynomial and Rational Functions
    • 4.1 Polynomial Functions
    • 4.2 Graphing Polynomial Functions; Models
    • 4.3 Properties of Rational Functions
    • 4.4 The Graph of a Rational Function
    • 4.5 Polynomial and Rational Inequalities
    • 4.6 The Real Zeros of a Polynomial Function
    • Chapter 4 Review, Test, and Projects
  5. Exponential and Logarithmic Functions
    • 5.1 Composite Functions
    • 5.2 One-to-One Functions; Inverse Functions
    • 5.3 Exponential Functions
    • 5.4 Logarithmic Functions
    • 5.5 Properties of Logarithms
    • 5.6 Logarithmic and Exponential Equations
    • 5.7 Financial Models
    • 5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
    • 5.9 Building Exponential, Logarithmic, and Logistic Models from Data
    • Chapter 5 Review, Test, and Projects
  6. Trigonometric Functions
    • 6.1 Angles, Arc, Length, and Circular Motion
    • 6.2 Trigonometric Functions: Unit Circle Approach
    • 6.3 Properties of the Trigonometric Functions
    • 6.4 Graphs of the Sine and Cosine Functions
    • 6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
    • 6.6 Phase Shift; Sinusoidal Curve Fitting
    • Chapter 6 Review, Test, and Projects
  7. Analytic Trigonometry
    • 7.1 The Inverse Sine, Cosine, and Tangent Functions
    • 7.2 The Inverse Trigonometric Functions (Continued)
    • 7.3 Trigonometric Equations
    • 7.4 Trigonometric Identities
    • 7.5 Sum and Difference Formulas
    • 7.6 Double-angle and Half-angle Formulas
    • 7.7 Product-to-Sum and Sum-to-Product Formulas
    • Chapter 7 Review, Test, and Projects
  8. Applications of Trigonometric Functions
    • 8.1 Right Triangle Trigonometry; Applications
    • 8.2 The Law of Sines
    • 8.3 The Law of Cosines
    • 8.4 Area of a Triangle
    • 8.5 Simple Harmonic Motion; Damped Motion; Combining Waves
    • Chapter 8 Review, Test, and Projects
  9. Polar Coordinates; Vectors
    • 9.1 Polar Coordinates
    • 9.2 Polar Equations and Graphs
    • 9.3 The Complex Plane; De Moivre’s Theorem
    • 9.4 Vectors
    • 9.5 The Dot Product
    • 9.6 Vectors in Space
    • 9.7 The Cross Product
    • Chapter 9 Review, Test, and Projects
  10. Analytic Geometry
    • 10.1 Conics
    • 10.2 The Parabola
    • 10.3 The Ellipse
    • 10.4 The Hyperbola
    • 10.5 Rotation of Axes; General Form of a Conic
    • 10.6 Polar Equations of Conics
    • 10.7 Plane Curves and Parametric Equations
    • Chapter 10 Review, Test, and Projects
  11. Systems of Equations and Inequalities
    • 11.1 Systems of Linear Equations: Substitution and Elimination
    • 11.2 Systems of Linear Equations: Matrices
    • 11.3 Systems of Linear Equations: Determinants
    • 11.4 Matrix Algebra
    • 11.5 Partial Fraction Decomposition
    • 11.6 Systems of Nonlinear Equations
    • 11.7 Systems of Inequalities
    • 11.8 Linear Programming
    • Chapter 11 Review, Test, and Projects
  12. Sequences; Induction; the Binomial Theorem
    • 12.1 Sequences
    • 12.2 Arithmetic Sequences
    • 12.3 Geometric Sequences; Geometric Series
    • 12.4 Mathematical Induction
    • 12.5 The Binomial Theorem
    • Chapter 12 Review, Test, and Projects
  13. Counting and Probability
    • 13.1 Counting
    • 13.2 Permutations and Combinations
    • 13.3 Probability
    • Chapter 13 Review, Test, and Projects
  14. A Preview of Calculus: The Limit, Derivative, and Integral of a Function
    • 14.1 Finding Limits Using Tables and Graphs
    • 14.2 Algebra Techniques for Finding Limits
    • 14.3 One-sided Limits; Continuous Functions
    • 14.4 The Tangent Problem; The Derivative
    • 14.5 The Area Problem; The Integral
    • Chapter 14 Review, Test, and Projects

Appendix A: Review

  • A.1 Algebra Essentials
  • A.2 Geometry Essentials
  • A.3 Polynomials
  • A.4 Synthetic Division
  • A.5 Rational Expressions
  • A.6 Solving Equations
  • A.7 Complex Numbers; Quadratic Equations in the Complex Number System
  • A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
  • A.9 Interval Notation; Solving Inequalities
  • A.10 nth Roots; Rational Exponents

Appendix B: Graphing Utilities

  • B.1 The Viewing Rectangle
  • B.2 Using a Graphing Utility to Graph Equations
  • B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
  • B.4 Using a Graphing Utility to Solve Equations
  • B.5 Square Screens
  • B.6 Using a Graphing Utility to Graph Inequalities
  • B.7 Using a Graphing Utility to Solve Systems of Linear Equations
  • B.8 Using a Graphing Utility to Graph a Polar Equation
  • B.9 Using a Graphing Utility to Graph Parametric Equations

Answers

Credits

Index

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