College Algebra Enhanced with Graphing Utilities

(NOTE: Each chapter concludes with Chapter Review.)

R. Review.


Real Numbers. Algebra Review. Geometry Review. Integer Exponents. Polynomials. Factoring Polynomials. Rational Expressions. Square Roots; Radicals. Rational Exponents.



1. Graphs.


Rectangular Coordinates; Graphing Utilities. Introduction to Graphing Equations. Solving Equations Using a Graphing Utility; Linear and Quadratic Equations. Setting up Equations; Applications. Radical Equations; Equations Quadratic in Form; Absolute Value Equations. Solving Inequalities. Lines. Circles. Chapter Projects.



2. Linear and Quadratic Functions.


Functions. Linear Functions and Models. Quadratic Functions. Quadratic Models. Chapter Projects. Cumulative Review.



3. Functions and Their Graphs.


Symmetry; Graphing Key Equations. Properties of Functions. Library of Functions; Piecewise-Defined Functions. Graphing Techniques: Transformations. Operations on Functions; Composite Functions. Mathematical Models: Constructing Functions. Chapter Projects. Cumulative Review.



4. Polynomial and Rational Functions.


Power Functions and Models. Polynomial Functions and Models. Rational Functions I. Rational Functions II: Analyzing Graphs. Polynomial and Rational Inequalities. Chapter Projects. Cumulative Review.



5. The Zeros of a Polynomial Function.


Synthetic Division. The Real Zeros of a Polynomial Function. Complex Numbers; Quadratic Equations with a Negative Discriminant. Complex Zeros; Fundamental Theorem of Algebra. Chapter Projects. Cumulative Review.



6. Exponential and Logarithmic Functions.


One-to-One Functions; Inverse Functions. Exponential Functions. Logarithmic Functions. Properties of Logarithms. Logarithmic and Exponential Equations. Compound Interest. Growth and Decay. Exponential, Logarithmic, and Logistic Curve Fitting. Chapter Projects. Cumulative Review.



7. Systems of Equations and Inequalities.


Systems of Linear Equations: Two Equations Containing Two Variables. Systems of Linear Equations: Three Equations Containing Three Variables. Systems of Linear Equations: Matrices. Systems of Linear Equations: Determinants. Matrix Algebra. Systems of Linear Inequalities; Linear Programming. Partial Fraction Decomposition. Chapter Projects. Cumulative Review.



8. Sequences; Induction; the Binomial Theorem.


Sequences. Arithmetic Sequences. Geometric Sequences; Geometric Series. Mathematical Induction. The Binomial Theorem. Chapter Projects. Cumulative Review.



9. Counting and Probability.


Sets and Counting. Permutations and Combinations. Probability of Equally Likely Outcomes. Obtaining Probabilities from Data. Chapter Projects. Cumulative Review.



10. Conics.


Preliminaries. The Parabola. The Ellipse. The Hyperbola. Systems of Nonlinear Equations. Chapter Projects. Cumulative Review.



Answers.


Index.