Precalculus Functions and Graphs – Ron Larson – 4th Edition

1. FUNCTIONS AND THEIR GRAPHS.
Introduction to Library of Functions.
Lines in the Plane.
Functions.
Graphs of Functions.
Shifting, Reflecting, and Stretching Graphs.
Combinations of Functions.
Inverse Functions.
Linear Models and Scatter Plots.

2. POLYNOMIAL AND RATIONAL FUNCTIONS.
Quadratic Functions.
Polynomial Functions of Higher Degree.
Real Zeros of Polynomial Functions.
Complex Numbers.
The Fundamental Theorem of Algebra.
Rational Functions and Asymptotes.
Graphs of Rational Functions.
Quadratic Models.

3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions and Their Graphs.
Logarithmic Functions and Their Graphs.
Properties of Logarithms.
Solving Exponential and Logarithmic Equations.
Exponential and Logarithmic Models.
Nonlinear Models.

4. TRIGONOMETRIC FUNCTIONS.
Radian and Degree Measure.
Trigonometric Functions: The Unit Circle.
Right Triangle Trigonometry.
Trigonometric Functions of Any Angle.
Graphs of Sine and Cosine Functions.
Graphs of Other Trigonometric Functions.
Inverse Trigonometric Functions.
Applications and Models.
Library of Parent Functions Review.

5. ANALYTIC TRIGONOMETRY.
Using Fundamental Identities.
Verifying Trigonometric Identities.
Solving Trigonometric Equations.
Sum and Difference Formulas.
Multiple-Angle and Product-to-Sum Formulas.

6. ADDITIONAL TOPICS IN TRIGONOMETRY.
Law of Sines.
Law of Cosines.
Vectors in the Plane.
Vectors and Dot Products.
Trigonometric Form of a Complex Number.

7. LINEAR SYSTEMS AND MATRICES.
Solving Systems of Equations.
Systems of Linear Equations in Two Variables.
Multivariable Linear Systems.
Matrices and Systems of Equations.
Operations with Matrices.
The Inverse of a Square Matrix.
The Determinant of a Square Matrix.
Applications of Matrices and Determinants.

8. SEQUENCES, SERIES, AND PROBABILITY.
Sequences and Series.
Arithmetic Sequences and Partial Sums.
Geometric Sequences and Series.
The Binomial Theorem.
Counting Principles.
Probability.

9. TOPICS IN ANALYTIC GEOMETRY.
Circles and Parabolas.
Ellipses. Hyperbolas and Rotation of Conics.
Parametric Equations.
Polar Coordinates.
Graphs of Polar Equations.
Polar Equations of Conics.