When introducing mathematical ideas, this book moves from the concrete to the abstract, rather than the reverse. It is the authors philosophy that learning is increased when students can relate a concept to something in their lives. This approach increases both interest and motivation. Students see the importance of a topic from a practical and intuitive point of view, with models and applications playing a central part in the learning process.
1. Introduction To Functions and Graphs.
Numbers, Data, and Problem Solving. 2. Linear Functions and Equations.
Visualization of Data.
Functions and Their Representations.
Types of Functions and Their Rates of Change.
Linear Functions and Models. 3. Quadratic Functions and Equations.
Equations of Lines.
Linear Equations and Problem Solving.
Piecewise-Defined Linear Functions.
Quadratic Functions and Models. 4. Nonlinear Functions and Equations.
Quadratic Equations and Problem Solving.
Transformations of Graphs.
Nonlinear Functions and Their Graphs. 5. Exponential and Logarithmic Functions.
Polynomial Functions and Models.
Real Zeros of Polynomial Functions.
The Fundamental Theorem of Algebra.
Rational Functions and Models.
Polynomial and Rational Inequalities.
Power Functions and Radical Equations .
Combining Functions. 6. Systems of Equations and Inequalities.
Inverse Functions and Their Representations.
Exponential Functions and Models.
Logarithmic Functions and Models.
Properties of Logarithms.
Exponential and Logarithmic Equations.
Constructing Nonlinear Models.
Functions and Equations of More Than One Variable. 7. Conic Sections.
Linear Systems of Equations and Inequalities in Two Variables.
Solutions of Linear Systems Using Matrices.
Properties and Applications of Matrices.
Inverses of Matrices.
Parabolas. 8. Further Topics in Algebra.
Sequences. R. Basic Algebraic Concepts.
The Binomial Theorem.
Formulas from Geometry. Appendix A: A Library of Functions. Appendix B: TI-83/Plus Graphing Calculators.