College Algebra

R. David Gustafson is professor emeritus of mathematics at Rock Valley College in Illinois and has also taught extensively at Rockford College and Beloit College. In addition to this best-selling college algebra resource with Jeffrey Hughes, he has co-authored Gustafson/Karr/Massey's BEGINNING ALGEBRA; INTERMEDIATE ALGEBRA; BEGINNING AND INTERMEDIATE ALGEBRA; BEGINNING AND INTERMEDIATE ALGEBRA: A COMBINED APPROACH; and the Tussy/Gustafson and Tussy/Gustafson/Koenig Developmental Mathematics series. His numerous professional honors include Rock Valley Teacher of the Year and Rockford's Outstanding Educator of the Year. He has been very active in the American Mathematical Association of Two-Year Colleges (AMATYC) as a Midwest vice president. He has also served as president of IMACC, AMATYC's Illinois affiliate. Professor Gustafson earned a master of arts from Rockford College in Illinois as well as a master of science from Northern Illinois University. Jeffrey Hughes is Curriculum Coordinator of Mathematics at Hinds Community College (Hinds CC) and holds degrees from Mississippi College and the University of Mississippi. He has been teaching for more than 30 years at Hinds CC. Professor Hughes' favorite courses to teach include college algebra, calculus II and differential equations. He has a passion for mathematics and a heart for student instruction, and he sees teaching as a privilege. Professor Hughes consistently finds new ways to present topics while engaging students and elevating student thinking. In addition to this edition, Professor Hughes has co-authored PRECALCULUS, published by Cengage. He has received Hinds CC’s Outstanding Academic Instructor of the Year Award and Hinds CC’s Phi Theta Kappa’s Teacher of the Year Award twice. He has been honored by the Mississippi Legislature for his commitment to education and has received the HEADWAE award. Professor Hughes is also active in the American Mathematical Association of Two-Year Colleges (AMATYC) and has served as a president of its Louisiana-Mississippi affiliate, LaMsMATYC. In addition, he is active in the Mississippi Collegiate Mathematics Association (MCMA) and has served as president of this organization twice. At Hinds CC, he teaches leadership in the Honors Institute. Professor Hughes has worked part-time for more than twenty-five years as a student minister at his church and has spent seven summers teaching English in China.

Chapter R. A REVIEW OF BASIC ALGEBRA.
Sets of Real Numbers. Integer Exponents and Scientific Notation. Rational Exponents and Radicals. Polynomials and Additional Properties of Radicals. Factoring. Rational Expressions. Chapter Review. Chapter Test. Group Activity: Anesthesiology.
1. EQUATIONS AND INEQUALITIES.
Linear Equations and Rational Equations. Applications of Linear and Rational Equations. Complex Numbers. Quadratic Equations. Applications of Quadratic Equations. Radical Equations and Equations Quadratic in Form. Linear, Compound, Quadratic, and Rational Inequalities. Absolute Value Equations and Inequalities. Chapter Review. Chapter Test. Cumulative Review. Group Activity: Health and Body Mass Index.
2. FUNCTIONS AND GRAPHS.
Functions and Functional Notation. Rectangular Coordinate System and Linear Functions. Slope and Its Applications. Writing Equations of Lines. Graphs of Equations and Circles. Proportion and Variation. Chapter Review. Chapter Test. Group Activity: Average Velocity.
3. FUNCTIONS.
Graphs of Functions. Transformations of the Graphs of Functions. More on Functions; Piecewise-Defined Functions. Combinations of Functions and Function Composition. Inverse functions. Chapter Review. Chapter Test. Cumulative Review. Group Activity: Cryptography and Cybersecurity.
4. POLYNOMIAL AND RATIONAL FUNCTIONS.
Quadratic Functions. Polynomial Functions. Synthetic Division; Remainder and Factor Theorems. Fundamental Theorem of Algebra and Descartes’ Rule Signs. Zeros of Polynomial Functions. Rational Functions. Chapter Review. Chapter Test. Group Activity: Polynomial Function Trending.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions and Their Graphs. Applications of Exponential Functions. Logarithmic Functions and Their Graphs. Applications of Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Chapter Review. Chapter Test. Cumulative Review. Group Activity: Group Activity - Installment Loans.
6. SYSTEMS OF LINEAR EQUATIONS, MATRICES, AND INEQUALITIES.
Systems of Linear Equations. Using Matrices to Solve Systems of Linear Equations. Matrix Operations. Multiplicative Inverses of Matrices and Matrix Equations. Determinants and Cramer's Rule. Partial Fractions. Inequalities and Systems of Inequalities in Two Variables. Linear Programming. Chapter Review. Chapter Test. Group Activity: Vacation Budget.
7. CONIC SECTIONS AND SYSTEMS OF NONLINEAR EQUATIONS.
The Circle and the Parabola. The Ellipse. The Hyperbola. Solving Nonlinear Systems of Equations. Chapter Review. Chapter Test. Cumulative Review. Group Activity: Suspension Bridges.
8. SEQUENCES, SERIES, INDUCTION AND PROBABILITY.
The Binomial Theorem. Sequences, Series, and Summation Notation. Arithmetic Sequences and Series. Geometric Sequences and Series. Mathematical Induction. Fundamental Counting Principle, Permutations, and Combinations. Introduction to Probability. Chapter Review. Chapter Test. Group Activity: Lottery Mathematics.
APPENDIX I A PROOF OF THE BINOMIAL THEOREM.