College Algebra: Concepts Through Functions, 4th edition

  • Michael Sullivan

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Overview

The Concepts Through Functions Series introduces functions at the start of each text -- and a new function in every chapter. The authors focus on the fundamentals to help you master basic skills and develop the conceptual understanding needed for this and future courses.

Published by Pearson (December 11th 2020) - Copyright © 2024

ISBN-13: 9780137399598

Subject: Precalculus, College Algebra & Trigonometry

Category: College Algebra

Table of contents

Table of Contents

  1. Foundations: A Prelude to Functions
    • F.1 The Distance and Midpoint Formulas
    • F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
    • F.3 Lines
    • F.4 Circles
  1. Functions and Their Graphs
    • 1.1 Functions
    • 1.2 The Graph of a Function
    • 1.3 Properties of Functions
    • 1.4 Library of Functions; Piecewise-defined Functions
    • 1.5 Graphing Techniques: Transformations
    • 1.6 Mathematical Models: Constructing Functions
    • 1.7 Building Mathematical Models Using Variation
    • Chapter Review
    • Chapter Test
    • Chapter Projects
  2. Linear and Quadratic Functions
    • 2.1 Properties of Linear Functions and Linear Models
    • 2.2 Building Linear Models from Data
    • 2.3 Quadratic Functions and Their Zeros
    • 2.4 Properties of Quadratic Functions
    • 2.5 Inequalities Involving Quadratic Functions
    • 2.6 Building Quadratic Models from Verbal Descriptions and from Data
    • 2.7 Complex Zeros of a Quadratic Function
    • 2.8 Equations and Inequalities Involving the Absolute Value Function
    • Chapter Review
    • Chapter Test
    • Chapter Projects
    • Cumulative Review
  3. Polynomial and Rational Functions
    • 3.1 Polynomial Functions and Models
    • 3.2 The Real Zeros of a Polynomial Function
    • 3.3 Complex Zeros; Fundamental Theorem of Algebra
    • 3.4 Properties of Rational Functions
    • 3.5 The Graph of a Rational Function
    • 3.6 Polynomial and Rational Inequalities
    • Chapter Review
    • Chapter Test
    • Chapter Projects
    • Cumulative Review
  4. Exponential and Logarithmic Functions
    • 4.1 Composite Functions
    • 4.2 One-to-One Functions; Inverse Functions
    • 4.3 Exponential Functions
    • 4.4 Logarithmic Functions
    • 4.5 Properties of Logarithms
    • 4.6 Logarithmic and Exponential Equations
    • 4.7 Compound Interest
    • 4.8 Exponential Growth and Decay; Newton’s Law; Logistic Growth and Decay
    • 4.9 Building Exponential, Logarithmic, and Logistic Functions from Data
    • Chapter Review
    • Chapter Test
    • Chapter Projects
    • Cumulative Review
  5. Conics
    • 5.1 Conics
    • 5.2 The Parabola
    • 5.3 The Ellipse
    • 5.4 The Hyperbola
    • Chapter Review
    • Chapter Test
    • Chapter Projects
    • Cumulative Review
  6. Systems of Equations and Inequalities
    • 6.1 Systems of Linear Equations: Substitution and Elimination
    • 6.2 Systems of Linear Equations: Matrices
    • 6.3 Systems of Linear Equations: Determinants
    • 6.4 Matrix Algebra
    • 6.5 Partial Fraction Decomposition
    • 6.6 Systems of Nonlinear Equations
    • 6.7 Systems of Inequalities
    • 6.8 Linear Programming
    • Chapter Review
    • Chapter Test
    • Chapter Projects
    • Cumulative Review
  7. Sequences; Induction; the Binomial Theorem
    • 7.1 Sequences
    • 7.2 Arithmetic Sequences
    • 7.3 Geometric Sequences; Geometric Series
    • 7.4 Mathematical Induction
    • 7.5 The Binomial Theorem
    • Chapter Review
    • Chapter Test
    • Chapter Projects
    • Cumulative Review
  8. Counting and Probability
    • 8.1 Counting
    • 8.2 Permutations and Combinations
    • 8.3 Probability
    • Chapter Review
    • Chapter Test
    • Chapter Projects
    • Cumulative Review

Appendix A. Review

  • A.1 Algebra Essentials
  • A.2 Geometry Essentials
  • A.3 Polynomials
  • A.4 Factoring Polynomials
  • A.5 Synthetic Division
  • A.6 Rational Expressions
  • A.7 nth Roots; Rational Exponents
  • A.8 Solving Equations
  • A.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs
  • A.10 Interval Notation; Solving Inequalities
  • A.11 Complex Numbers

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

Index

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