1. Numbers and Their Disguises.
Fractions, decimals, percent, powers, roots, scientific notation, calculators, rounding, intervals.
2. Solving Equations.
Equations of degree 1 and 2, the zero-factor property.
3. Introducing Functions and Graphs.
Various types of graphs, functions, domain and range, equations of lines, power functions, shifting, intersection of curves.
4. Changing the Form of a Function.
Factoring, canceling, rationalizing, extracting a factor from under a root.
5. Simplifying Algebraic Expressions.
Working with difference quotients and rational functions, canceling common factors, rationalizing expressions.
6. Composition and Decomposition of Functions.
Composite functions, inner, outer, and outermost functions, decomposing composite functions.
7. Equations of Degree 1 Revisited.
Solving linear equations involving derivatives.
8. Word Problems.
The geometry of rectangles, triangles, and circles, expressing one quantity as a function of one or more other quantities.
9. Exponential and Logarithmic Functions.
Working with graphs, expressions and equations of exponential functions, inverse functions, and logarithmic functions.
A. Completing the Square and Deriving the Quadratic Formula.
C. The Binomial Theorem.
Answers to Exercises.