Precalculus

1. FUNDAMENTALS. Sets of Real Numbers. Absolute Value. Solving Equations (Review and Preview). Rectangular Coordinates. Visualizing Data. Graphs and Graphing Utilities. Equations of Lines. Symmetry and Graphs. Circles. 2. EQUATIONS AND INEQUALITIES. Quadratic Equations: Theory and Examples. Other Types of Equations. Inequalities. More on Inequalities. 3. FUNCTIONS. The Definition of a Function. The Graph of a Function. Shapes of Graphs. Average Rate of Change. Techniques in Graphing. Methods of Combining Functions. Iteration. Inverse Functions. 4. POLYNOMIAL AND RATIONAL FUNCTIONS: APPLICATIONS TO OPTIMIZATION. Linear Functions. Quadratic Functions. Using Iteration to Model Populations Growth (Optional Section). Setting Up Equations That Devine Functions. Maximum and Minimum Problems. Polynomial Functions. Rational Functions. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. The Exponential Function y = ex. Logarithmic Functions. Properties of Logarithms. Equations and Inequalities with Logs and Exponents. Compound Interest. Exponential Growth and Decay. 6. AN INTRODUCTION TO TRIGONOMETRY VIA RIGHT TRIANGLES. Trigonometric Functions of Acute Angles. Right-Triangle Applications. Trigonometric Functions of Angles. Trigonometric Identities. 7. THE TRIGONOMETRIC FUNCTIONS. Radian Measure. Trigonometric Functions of Angles. Evaluating the Trigonometric Functions. Algebra and the Trigonometric Functions. Right-Triangle Trigonometry. 8. GRAPHS OF TRIGONOMETRIC FUNCTIONS. Trigonometric Functions of Real Numbers. Graphs of the Sine and Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx-C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions. 9. ANALYTICAL TRIGONOMETRY. The Addition Formulas. The Double-Angle Formulas. The Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations. The Inverse Trigonometric Functions. 10. ADDITIONAL TOPICS IN TRIGONOMETRY. Right-Triangle Applications. The Law of Sines and the L