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College Algebra: Concepts Through Functions, 5th edition

Published by Pearson (December 7, 2022) © 2024

  • Michael Sullivan Chicago State University
  • Michael Sullivan Joliet Junior College

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For courses in College Algebra.

Ties concepts together using a functions approach 

College Algebra: Concepts Through Functions, 5th Edition introduces functions at the beginning of the text, then introduces and develops a new function in every chapter. Acclaimed authors Sullivan and Sullivan focus on the fundamentals (preparing for class, practicing with homework, and reviewing key concepts), which encourages students to master basic skills and develop the conceptual understanding needed for this and future courses. Graphing utility coverage is optional and can be adjusted at the instructor's discretion, based on course needs.

Hallmark features of this title

  • Just-in-time review starts each section: Preparing for This Section lists earlier concepts that will be useful for the section ahead. Now Work "Are You Prepared?" problems help students assess their understanding.
  • Now Work problems: If students get stuck during homework, they can look for the closest Now Work problem and refer back to the related example.
  • Step-by-Step, Annotated Examples have detailed intermediate steps with annotations to help students see nuances.
  • Assess Your Understanding at the end of every section contains a variety of problems for skill mastery.
  • Skill Development problems are organized by difficulty and correlated to section examples.
  • DWR (Discussion, Writing and Research) problems are marked by an icon and red numbers. They support class discussion, verbalization of mathematical ideas, and writing and research projects.

New and updated features of this title

  • NEW: Challenge Problems in the Applications and Extensions part of the section exercises; full solutions are in the back of the Annotated Instructor's Edition and in the Instructor's Solution Manual.
  • NEW: Need to Review? reminders in the margin for key review topics point students to the review material in the textbook.
  • REVISED: Enhanced Chapter Projects are provided, many of which require students to research current information online to solve problems.
  • NEW: Interactive Figure Exercises (created by author Michael Sullivan III in GeoGebra) are marked with an icon and require students to manipulate an interactive figure to solve. Interactive figures are found online or in the Video & Resource Library of MyLab Math.
  • EXPANDED: Retain Your Knowledge Problems are based on learning research and increased in this edition by popular demand. Their focus on skill maintenance is retained, but many added problems preview skills required in later precalculus material or in calculus.
  • EXPANDED: Graphing utility screen captures in several instances include Desmos and GeoGebra screen images, along with the TI-84 Plus CE captures. This provides alternative ways of visualizing concepts and making connections between equations, data and graphs in full color.

Features of MyLab Math for the 5th Edition

  • NEW: Corequisite course support assists various corequisite course models, including Concurrent (just-in-time) and Consecutive (front-loaded). Along with the complete Corequisite eText built from Michael Sullivan III's developmental mathematics text, support includes:
    • Instructional videos for each corequisite objective, many featuring Michael Sullivan III in the classroom; Assignable algorithmic exercises for each corequisite objective
    • Worksheets with instruction and exercises for each corequisite objective (also available in print); Activities for selected corequisite objectives; Study Skills videos for time management, mindset, stress management, college transition, and more; and a Corequisite Implementation Guide.
  • UPDATED: MyLab exercises have been reviewed and edited thoroughly by Michael Sullivan III, to better match the text's language and approach and to make the solutions more student-friendly.
  • NEW: Instructional Videos: Every instructional video is new, created exclusively for this product. All videos are close-captioned and in high definition to be clearly readable on phones. Interactive Figures help students visualize key concepts. Handwriting is used to show examples worked out by hand, to accommodate the preference of most students.
  • NEW: Video Note-Taking Guide (written specifically for this program by Kevin Bodden and Randy Gallaher at Lewis and Clark Community College) helps students learn actively while watching videos.

Applications Index

F. 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 Building Mathematical Models from Verbal Descriptions
  • 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
  • Cumulative Review
  • Chapter Projects

3. Polynomial and Rational Functions

  • 3.1 Polynomial Functions
  • 3.2 Graphing Polynomial Functions: Models
  • 3.3 The Real Zeros of a Polynomial Function
  • 3.4 Complex Zeros; Fundamental Theorem of Algebra
  • 3.5 Properties of Rational Functions
  • 3.6 The Graph of a Rational Function
  • 3.7 Polynomial and Rational Inequalities
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

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 Financial Models
  • 4.8 Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay Models
  • 4.9 Building Exponential, Logarithmic, and Logistic Models from Data
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

5. Analytic Geometry

  • 5.1 Conics
  • 5.2 The Parabola
  • 5.3 The Ellipse
  • 5.4 The Hyperbola
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

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
  • Cumulative Review
  • Chapter Projects

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
  • Cumulative Review
  • Chapter Projects

8. Counting and Probability

  • 8.1 Counting
  • 8.2 Permutations and Combinations
  • 8.3 Probability
  • Chapter Review
  • Chapter Test
  • Cumulative Review
  • Chapter Projects

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 Job Applications
  • 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
Answers
Challenge Problem Solutions
Subject Index

About our authors

Michael Sullivan, Emeritus Professor of Mathematics at Chicago State University, received a Ph.D. in mathematics from the Illinois Institute of Technology. He is a native of Chicago's South Side and divides his time between Oak Lawn, Illinois and Naples, Florida.

Mike is a member of the American Mathematical Society and the Mathematical Association of America. He is a past president of the Text and Academic Authors Association and is currently Treasurer of its Foundation. He is a member of the TAA Council of Fellows, and was awarded the TAA Mike Keedy award in 1997 and the Lifetime Achievement Award in 2007. In addition, he represents TAA on the Authors Coalition of America. He has been writing textbooks for more than 35 years and currently has 15 books in print, 12 with Pearson Education. When not writing he enjoys tennis, golf, gardening and travel.

Mike has 4 children: Kathleen teaches college mathematics; Michael III teaches college mathematics and is his co-author on 2 precalculus series; Dan works in publishing; and Colleen teaches middle school and secondary school mathematics. 12 grandchildren round out the family.

Mike Sullivan III  is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of 3 children and an avid golfer, who tries to spend as much of his limited free time as possible on the golf course.

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