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Chapter 1: Preparing for Your Journey
Opening 
1.OP 
Chapter Opening 
Section 1.1 
1.1.1 
Interpreting Graphs 

1.1.2 
The Spring Problem 

1.1.3 
Modeling with Functions 

1.1.4 
Rates of Change 

1.1.5 
Setting Up Word Problems 

1.1.6 
Equivalent Expressions 
Section 1.2 
1.2.1 
Composition of Functions 

1.2.2 
Inverse Functions 

1.2.3 
PiecewiseDefined Functions and Continuity 
Section 1.3 
1.3.1 
Radians as a Unit of Measure 

1.3.2 
Radian Measure in the Unit Circle 

1.3.3 
Applications of Radian Measure 
Closure 
1.CL 
Chapter Closure 
Chapter 2: Functions and Trigonometry
Opening 
2.OP 
Chapter Opening 
Section 2.1 
2.1.1 
Characteristics of Functions 

2.1.2 
Evan and Odd Functions 

2.1.3 
Transformations of Functions 
Section 2.2 
2.2.1 
Special Angles in the Unit Circle 

2.2.2 
Trigonometric Ratios in the Unit Circle 

2.2.3 
Graphs of Sine and Cosine 

2.2.4 
Transformations of Sine and Cosine 

2.2.5 
Horizontal Stretches of Sine and Cosine Graphs 
Section 2.3 
2.3.1 
Solving Trigonometric Equations 

2.3.2 
Inverse Sine and Cosine 

2.3.3 
Graphs of Tangent and Inverse Tangent 
Closure 
2.CL 
Chapter Closure 
Chapter 3: Algebra and Area Under a Curve
Opening 
3.OP 
Chapter Opening 
Section 3.1 
3.1.1 
Operations with Rational Expressions 

3.1.2 
Rewriting Expressions and Equations 

3.1.3 
Solving Nonlinear Systems of Equations 

3.1.4 
Polynomial Division 

3.1.5 
Solving Classic Word Problems 
Section 3.2 
3.2.1 
Using Sigma Notation 

3.2.2 
Area Under a Curve: Part One 

3.2.3 
Area Under a Curve: Part Two 

3.2.4 
Area Under a Curve: Part Three 
Closure 
3.CL 
Chapter Closure 
Chapter 4: Polynomial and Rational Functions
Opening 
4.OP 
Chapter Opening 
Section 4.1 
4.1.1 
Graphs of Polynomial Functions in Factored Form 

4.1.2 
Writing Equations of Polynomial Functions 

4.1.3 
Writing Equations Using Complex Roots 
Section 4.2 
4.2.1 
Graphing Transformations of y = 1/x 

4.2.2 
Graphing Rational Functions 

4.2.3 
Graphing Reciprocal Functions 

4.3.1 
Polynomial and Rational Inequalities 

4.3.2 
Applications of Polynomial and Rational Functions 
Closure 
4.CL 
Chapter Closure 
Chapter 5: Exponentials and Logarithms
Opening 
5.OP 
Chapter Opening 
Section 5.1 
5.1.1 
Applications of Exponential Functions 

5.1.2 
Stretching Exponential Functions 

5.1.3 
The number e 
Section 5.2 
5.2.1 
Logarithms 

5.2.2 
Properties of Logarithms 

5.2.3 
Solving Exponential and Logarithmic Equations 

5.2.4 
Graphing Logarithmic Functions 

5.2.5 
Applications of Exponentials and Logarithms 
Closure 
5.CL 
Chapter Closure 
Chapter 6: Triangles and Vectors
Opening 
6.OP 
Chapter Opening 
Section 6.1 
6.1.1 
The Law of Sines and Area 

6.1.2 
Law of Cosines 

6.1.3 
The Ambiguous Case of the Law of Sines 
Section 6.2 
6.2.1 
An Introduction to Vectors 

6.2.2 
Operations with Vectors 

6.2.3 
Applications of Vectors 

6.2.4 
The Dot Product 
Closure 
6.CL 
Chapter Closure 
Chapter 7: Limits and Rates
Opening 
7.OP 
Chapter Opening 
Section 7.1 
7.1.1 
An Introduction to Limits 

7.1.2 
Working With OneSided Limits 

7.1.3 
The Definition of a Limit 

7.1.4 
Limits and Continuity 

7.1.5 
Special Limits 
Section 7.2 
7.2.1 
Rates of Change From Data 

7.2.2 
Slope and Rates of Change 

7.2.3 
Average Velocity and Rates of Change 

7.2.4 
Moving From AROC to IROC 

7.2.5 
Rate of Change Applications 
Closure 
7.CL 
Chapter Closure 
Chapter 8: Extending Periodic Functions
Opening 
8.OP 
Chapter Opening 
Section 8.1 
8.1.1 
Graphing y = asin(b(x – h))+ k 

8.1.2 
Modeling With Periodic Functions 

8.1.3 
Improving the Spring Problem 
Section 8.2 
8.2.1 
Graphing Reciprocal Trigonometric Functions 

8.2.2 
Trigonometric Functions, Geometrically (optional) 
Section 8.3 
8.3.1 
Simplifying Trigonometric Expressions 

8.3.2 
Proving Trigonometric Identities 

8.3.3 
Angle Sum and Difference Identities 

8.3.4 
DoubleAngle and HalfAngle Identities 

8.3.5 
Solving Complex Trigonometric Equations 
Closure 
8.CL 
Chapter Closure 
Chapter 9: Matrices
Opening 
9.OP 
Chapter Opening 
Section 9.1 
9.1.1 
Introduction to Matrices


9.1.2 
Matrix Multiplication


9.1.3 
Determinants and Inverse Matrices


9.1.4 
Solving Systems Using Matrix Equations

Section 9.2 
9.2.1 
Linear Transformations


9.2.2 
Composition of Transformations


9.2.3 
Properties of Linear Transformations

Closure 
9.CL 
Chapter Closure 
Chapter 10: Conics and Parametric Functions
Opening 
10.OP 
Chapter Opening 
Section 10.1 
10.1.1 
Circles and Completing the Square 

10.1.2 
Ellipses 

10.1.3 
Hyperbolas 

10.1.4 
Parabolas 

10.1.5 
Identifying Conic Sections 
Section 10.2 
10.2.1 
Introduction to ParametricallyDefined Functions


10.2.2 
Applications of Parametric Equations


10.2.3 
Conic Sections in Parametric Form

Closure 
10.CL 
Chapter Closure 
Chapter 11: Polar Functions and Complex Numbers
Opening 
11.OP 
Chapter Opening 
Section 11.1 
11.1.1 
Plotting Polar Coordinates


11.1.2 
Graphs of Polar Functions


11.1.3 
Families of Polar Functions


11.1.4 
Converting Between Polar and Rectangular Forms

Section 11.2 
11.2.1 
Using the Complex Plane


11.2.2 
Polar Form of Complex Numbers


11.2.3 
Operations with Complex Numbers in Polar Form


11.2.4 
Powers and Roots of Complex Numbers

Closure 
11.CL 
Chapter Closure 
Chapter 12: Series and Statistics
Opening 
12.OP 
Chapter Opening 
Section 12.1 
12.1.1 
Arithmetic Series


12.1.2 
Geometric Series


12.1.3 
Infinite Geometric Series


12.1.4 
Applications of Geometric Series


12.1.5 
The Sum of the Harmonic Series (optional)

Section 12.2 
12.2.1 
The Binomial Theorem 

12.2.2 
Binomial Probabilities 
Section 12.3 
12.3.1 
Mean and Expected Value of a Discrete Random Variable 

12.3.2 
Expected Value and Decision Making 
Closure 
12.CL 
Chapter Closure 
Chapter 13: Precalculus Finale
Opening 
13.OP 
Chapter Opening 
Section 13.1 
13.1.1 
A Race to Infinity 

13.1.2 
Limits to Infinity 

13.1.3 
Evaluating Limits at a Point Algebraically 

13.1.4 
Another Look at e 
Section 13.2 
13.2.1 
Trapping Area With Trapezoids 

13.2.2 
Area as a Function 

13.2.2A 
Going all to Pieces: Writing an Area Program 

13.2.3 
Rocket Launch 
Section 13.3 
13.3.1 
Velocity and Position Graphs 

13.3.2 
Instantaneous Velocity 

13.3.3 
Slope Functions 

13.3.4 
The Definition of Derivative 

13.3.5 
Slope and Area Under a Curve 
Closure 
13.CL 
Chapter Closure 