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(Each chapter (except Chapter R) concludes with a Chapter Summary, Review Exercises, Chapter Test, and Student Project.)
1. Rectangular Coordinates, Functions, and Analysis of Linear Functions.
Real Numbers, Logic, and Coordinate Systems.
Introduction to Relations and Functions.
Equations of Lines and Geometric Considerations.
Solution of Linear Equations; Analytic Method and Graphical Support.
Solution of Linear Inequalities; Analytic Method and Graphical Support.
Other Applications of Linear Functions.
2. Analysis of Graphs of Functions.
Graphs of Elementary Functions and Relations.
Vertical and Horizontal Shifts of Graphs of Functions.
Stretching, Shrinking, and Reflecting Graphs of Functions.
The Absolute Value Function: Graphs, Equations, Inequalities, and Applications.
Piecewise Defined Functions.
Further Topics in the Study of Functions
3. Polynomial Functions.
Quadratic Functions and Their Graphs.
Solution of Quadratic Equations and Inequalities.
Applications of Quadratic Functions and Models.
Higher Degree Polynomial Functions and Their Graphs.
Topics in the Theory of Polynomial Functions (I).
Topics in the Theory of Polynomial Functions (II).
Solution of Polynomial Equations and Inequalities and Their Applications.
4. Rational and Root Functions; Inverse Functions.
Graphs of Rational Functions.
Rational Equations, Inequalities, and Applications.
Graphs of Root Functions.
Root Equations, Inequalities, and Applications.
5.Exponential and Logarithmic Functions.
Introduction to Exponential Functions.
Logarithms and Their Properties.
Introduction to Logarithmic Functions.
Exponential and Logarithmic Equations and Inequalities.
Applications and Modeling with Exponential and Logarithmic Functions.
6. The Conic Sections and Parametric Equations.
Circles and Parabolas.
Ellipses and Hyperbolas.
Summary of the Conic Sections.
7. Matrices and Systems of Equations and Inequalities.
Systems of Equations.
Solution of Linear Systems by the Echelon Method.
Solution of Linear Systems by Row Transformations.
Properties of Matrices.
Determinants and Cramer's Rule.
Solution of Linear Systems by Matrix Inverses.
Systems of Inequalities and Linear Programming.
8. Further Topics in Algebra.
Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
The Binomial Theorem.
R. Reference: Basic Algebraic Concepts.
Review of Rules for Exponents and Operations with Polynomials.
Review of Factoring.
Review of Operations with Rational Expressions.
Review of Negative and Rational Exponents.
Review of Radicals.