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1. FUNCTIONS | |
Introduction | |
The Real Line | |
Inequalities | |
Intervals | |
Absolute Values | |
The Coordinate Plane | |
Distance Between Points in the Plane | |
Circles in the Plane | |
Completing the Square | |
Equations and Graphs | |
Graphs of Equations | |
Symmetry of a Graph | |
Using Technology to Graph Equations | |
Functions | |
Applications of Functions | |
Linear Functions | |
Parallel and Perpendicular Lines | |
Quadratic Functions | |
The Standard Form of a Quadratic Equation | |
The Quadratic Formula | |
2. NEW FUNCTIONS FROM OLD | |
Introduction | |
Other Common Functions | |
The Absolute Value Function | |
The Square Root Function | |
The Greatest Integer Function | |
Arithmetic Combinations of Functions | |
Composition of Functions | |
Inverse Functions | |
3. ALGEBRAIC FUNCTIONS | |
Introduction | |
Polynomial Functions | |
Finding Factors and Zeros of Polynomials | |
The Rational Zero Test | |
Rational Functions | |
Other Algebraic Functions | |
Complex Roots of Polynomials | |
4. TRIGONOMETRIC FUNCTIONS | |
Introduction | |
Measuring Angles | |
Length of a Circular Arc | |
Area of a Circular Sector | |
The Sine and Cosine Functions | |
Graphs of the Sine and Cosine Functions | |
Other Trigonometric Functions | |
The Graph of the Tangent Function | |
Trigonometric Identities | |
Pythagorean Identities | |
Sum and Difference Formulas | |
Double Angle Formulas | |
Half Angle Formulas | |
Products of Sines and Cosines | |
Right-Triangle Trigonometry | |
Inverse Trigonometric Functions | |
Applications of Trigonometric Functions | |
Law of Cosines | |
Law of Sines | |
Simple Harmonic Motion | |
Heron's Formula | |
5. EXPONENTIAL AND LOGARITHM FUNCTIONS | |
Introduction | |
The Natural Exponential Function | |
Compound Interest | |
Logarithm Functions | |
Exponential Growth and Decay | |
6. CONIC SECTIONS, POLAR COORDINATES, AND PARAMETRIC EQUATIONS | |
Introduction | |
Parabolas | |
Ellipses | |
Hyperbolas | |
Polar Coordinates | |
Graphs of Polar Equations | |
Conic Sections in Polar Coordinates | |
Parametric Equations |