## Table of Contents

1. Functions

1.1 Functions and function notation

1.2 Domain and range

1.3 Rates of change and behavior of graphs

1.4 Composition of functions

1.5 Transformation of functions

1.6 Absolute value functions

1.7 Inverse functions

2. Linear Functions

2.1 Linear functions

2.2 Graphs of linear functions

2.3 Modeling with linear functions

2.4 Fitting linear models to data

3. Polynomial and Rational Functions

3.1 Complex numbers

3.2 Quadratic functions

3.3 Power functions and polynomial functions

3.4 Graphs of polynomial functions

3.5 Dividing polynomials

3.6 Zeros of polynomial functions

3.7 Rational functions

3.8 Inverses and radical functions

3.9 Modeling using variation

4. Exponential and Logarithmic Functions

4.1 Exponential functions

4.2 Graphs of exponential functions

4.3 Logarithmic functions

4.4 Graphs of logarithmic functions

4.5 Logarithmic properties

4.6 Exponential and logarithmic equations

4.7 Exponential and logarithmic models

4.8 Fitting exponential models to data

5. Trigonometric Functions

5.1 Angles

5.2 Unit circle: sine and cosine functions

5.3 The other trigonometric functions

5.4 Right triangle trigonometry

6. Periodic Functions

6.1 Graphs of the sine and cosine functions

6.2 Graphs of the other trigonometric functions

6.3 Inverse trigonometric functions

7. Trigonometric Identities and Equations

7.1 Verifying trigonometric identities

7.2 Sum and difference identities

7.3 Double-angle, half-angle, and reduction formulas

7.4 Sum-to-product and product-to-sum formulas

7.5 Solving trigonometric equations

7.6 Modeling with trigonometric equations

8. Further Applications of Trigonometry

8.1 Non-right triangles: Law of sines

8.2 Non-right triangles: Law of cosines

8.3 Polar coordinates

8.4 Polar coordinates: Graphs

8.5 Polar form of complex numbers

8.6 Parametric equations

8.7 Parametric equations: Graphs

8.8 Vectors

9. Systems of Equations and Inequalities

9.1 Systems of linear equations: Two variables

9.2 Systems of linear equations: Three variables

9.3 Systems of nonlinear equations and inequalities: Two variables

9.4 Partial fractions

9.5 Matrices and matrix operations

9.6 Solving systems with Gaussian elimination

9.7 Solving systems with inverses

9.8 Solving systems with Cramer’s rule

10. Analytic Geometry

10.1 The ellipse

10.2 The hyperbola

10.3 The parabola

10.4 Rotation of axes

10.5 Conic sections in polar coordinates

11. Sequences, Probability and Counting Theory

11.1 Sequences and their notations

11.2 Arithmetic sequences

11.3 Geometric sequences

11.4 Series and their notations

11.5 Counting principles

11.6 Binomial theorem

11.7 Probability

12. Introduction to Calculus

12.1 Finding limits: Numerical and graphical approaches

12.2 Finding limits: Properties of limits

12.3 Continuity

12.4 Derivatives

13. Appendix: Basic Functions and Identities

13.1 Graphs of the parent functions

13.2 Graphs of the trigonometric functions

13.3 Trigonometric identities

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- More than 5000 end-of-section exercises

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