Algebra and Trigonometry Enhanced with Graphing Utilities, 8th edition

  • Michael Sullivan

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Overview

Algebra and Trigonometry Enhanced with Graphing Utilities takes a practical approach to integrating graphing tools and techniques into an exploration of advanced math concepts.

Published by Pearson (September 1st 2020) - Copyright © 2021

ISBN-13: 9780136872795

Subject: Precalculus, College Algebra & Trigonometry

Category: Algebra & Trigonometry

Table of contents

Table of Contents

  1. Review
    • R.1 Real Numbers
    • R.2 Algebra Essentials
    • R.3 Geometry Essentials
    • R.4 Polynomials
    • R.5 Factoring Polynomials
    • R.6 Synthetic Division
    • R.7 Rational Expressions
    • R.8 n th Roots; Rational Exponents
  1. Graphs, Equations, and Inequalities
    • 1.1 Graphing Utilities; Introduction to Graphing Equations
    • 1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations
    • 1.3 Quadratic Equations
    • 1.4 Complex Numbers; Quadratic Equations in the Complex Number System
    • 1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations; Factorable Equations
    • 1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
    • 1.7 Solving Inequalities
  2. Graphs
    • 2.1 The Distance and Midpoint Formulas
    • 2.2 Intercepts: Symmetry; Graphing Key Equations
    • 2.3 Lines
    • 2.4 Circles
    • 2.5 Variation
  3. Functions and Their Graphs
    • 3.1 Functions
    • 3.2 The Graph of a Function
    • 3.3 Properties of Functions
    • 3.4 Library of Functions; Piecewise-defined Functions
    • 3.5 Graphing Techniques: Transformations
    • 3.6 Mathematical Models: Building Functions
  4. Linear and Quadratic Functions
    • 4.1 Properties of Linear Functions and Linear Models
    • 4.2 Building Linear Models from Data
    • 4.3 Quadratic Functions and Their Properties
    • 4.4 Build Quadratic Models from Verbal Descriptions and from Data
    • 4.5 Inequalities Involving Quadratic Functions
  5. Polynomial and Rational Functions
    • 5.1 Polynomial Functions
    • 5.2 The Graph of a Polynomial Function; Models
    • 5.3 The Real Zeroes of a Polynomial Function
    • 5.4 Complex Zeroes: Fundamental Theorem of Algebra
    • 5.5 Properties of Rational Functions
    • 5.6 The Graph of a Rational Function
    • 5.7 Polynomial and Rational Inequalities
  6. Exponential and Logarithmic Functions
    • 6.1 Composite Functions
    • 6.2 One-to-One Functions; Inverse Functions
    • 6.3 Exponential Functions
    • 6.4 Logarithmic Functions
    • 6.5 Properties of Logarithms
    • 6.6 Logarithmic and Exponential Equations
    • 6.7 Financial Models
    • 6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
    • 6.9 Building Exponential, Logarithmic, and Logistic Models from Data
  7. Trigonometric Functions
    • 7.1 Angles and Their Measure
    • 7.2 Right Triangle Trigonometry
    • 7.3 Computing the Values of Trigonometric Functions of Acute Angles
    • 7.4 Trigonometric Functions of Any Angle
    • 7.5 Unit Circle Approach; Properties of the Trigonometric Functions
    • 7.6 Graphs of the Sine and Cosine Functions
    • 7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
    • 7.8 Phase Shift; Sinusoidal Curve Fitting
  8. Analytic Trigonometry
    • 8.1 The Inverse Sine, Cosine, and Tangent Functions
    • 8.2 The Inverse Trigonometric Functions (Continued)
    • 8.3 Trigonometric Equations
    • 8.4 Trigonometric Identities
    • 8.5 Sum and Difference Formulas
    • 8.6 Double-angle and Half-angle Formulas
    • 8.7 Product-to-Sum and Sum-to-Product Formulas
  9. Applications of Trigonometric Functions
    • 9.1 Applications Involving Right Triangles
    • 9.2 The Law of Sines
    • 9.3 The Law of Cosines
    • 9.4 Area of a Triangle
    • 9.5 Simple Harmonic Motion; Damped Motion; Combining Waves
  10. Polar Coordinates; Vectors
    • 10.1 Polar Coordinates
    • 10.2 Polar Equations and Graphs
    • 10.3 The Complex Plane; De Moivre’s Theorem
    • 10.4 Vectors
    • 10.5 The Dot Product
  11. Analytic Geometry
    • 11.1 Conics
    • 11.2 The Parabola
    • 11.3 The Ellipse
    • 11.4 The Hyperbola
    • 11.5 Rotation of Axes; General Form of a Conic
    • 11.6 Polar Equations of Conics
    • 11.7 Plane Curves and Parametric Equations
  12. Systems of Equations and Inequalities
    • 12.1 Systems of Linear Equations: Substitution and Elimination
    • 12.2 Systems of Linear Equations: Matrices
    • 12.3 Systems of Linear Equations: Determinants
    • 12.4 Matrix Algebra
    • 12.5 Partial Fraction Decomposition
    • 12.6 Systems of Nonlinear Equations
    • 12.7 Systems of Inequalities
    • 12.8 Linear Programming
  13. Sequences; Induction; the Binomial Theorem
    • 13.1 Sequences
    • 13.2 Arithmetic Sequences
    • 13.3 Geometric Sequences; Geometric Series
    • 13.4 Mathematical Induction
    • 13.5 The Binomial Theorem
  14. Counting and Probability
    • 14.1 Counting
    • 14.2 Permutations and Combinations
    • 14.3 Probability

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