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Chapter 1: Investigations and Functions
Opening 
1.OP 
Chapter Opening 
Section 1.1 
1.1.1 
Solving Puzzles in Teams 

1.1.2 
Using a Graphing Calculator to Explore a Function 

1.1.3 
Domain and Range 

1.1.4 
Points of Intersection in Multiple Representations 
Section 1.2 
1.2.1 
Modeling a Geometric Relationship 

1.2.2 
Function Investigation 

1.2.3 
The Family of Linear Functions 

1.2.4 
Function Investigation Challenge 
Closure 
1.CL 
Chapter Closure 
Chapter 2: Sequences and Equivalence
Opening 
2.OP 
Chapter Opening 
Section 2.1 
2.1.1 
Representing Exponential Growth 

2.1.2 
Rebound Ratio 

2.1.3 
The Bouncing Ball and Exponential Decay 

2.1.4 
Generating and Investigating Sequences 

2.1.5 
Generalizing Arithmetic Sequences 

2.1.6 
Using Multipliers to Solve Problems 

2.1.7 
Comparing Sequences and Functions 

2.1.8 
Sequences that Begin with n = 1 
Section 2.2 
2.2.1 
Equivalent Expressions 

2.2.2 
Area Models and Equivalent Expressions 

2.2.3 
Solving by Rewriting 
Closure 
2.CL 
Chapter Closure 
Chapter 3: Exponential Functions
Opening 
3.OP 
Chapter Opening 
Section 3.1 
3.1.1 
Investigating y = b^{x} 

3.1.2 
Multiple Representations 

3.1.3 
More Applications of Exponential Growth 

3.1.4 
Exponential Decay 

3.1.5 
Graph to Rule 

3.1.6 
Completing the Web 
Section 3.2 
3.2.1 
Curve Fitting and Fractional Exponents 

3.2.2 
More Curve Fitting 

3.2.3 
Solving a System of Exponential Functions Graphically 
Closure 
3.CL 
Chapter Closure 
Chapter 4: Transformations of Parent Graphs
Opening 
4.OP 
Chapter Opening 
Section 4.1 
4.1.1 
Modeling NonLinear Data 

4.1.2 
Parabola Investigation 

4.1.3 
Graphing a Parabola Without a Table 

4.1.4 
Mathematical Modeling with Parabolas 
Section 4.2 
4.2.1 
Transforming Other Parent Graphs 

4.2.2 
Describing (h, k) for Each Family of Functions 

4.2.3 
Transforming the Absolute Value Parent Graph 

4.2.4 
Transforming NonFunctions 
Section 4.3 
4.3.1 
Completing the Square 

4.3.2 
More Completing the Square 
Closure 
4.CL 
Chapter Closure 
Chapter 5: Solving and Intersections
Opening 
5.OP 
Chapter Opening 
Section 5.1 
5.1.1 
Strategies for Solving Equations 

5.1.2 
Solving Equations and Systems Graphically 

5.1.3 
Finding Multiple Solutions to Systems of Equations 

5.1.4 
Using Systems of Equations to Solve Problems 
Section 5.2 
5.2.1 
Solving Inequalities with One or Two Variables 

5.2.2 
Using Systems to Solve a Problem 

5.2.3 
Applications of Systems of Linear Inequalities 

5.2.4 
Using Graphs to Find Solutions 
Closure 
5.CL 
Chapter Closure 
Chapter 6: Inverses and Logarithms
Opening 
6.OP 
Chapter Opening 
Section 6.1 
6.1.1 
Undo Rules 

6.1.2 
Using a Graph to Find the Inverse 

6.1.3 
Finding Inverses and Justifying Algebraically 
Section 6.2 
6.2.1 
Finding the Inverse of an Exponential Function 

6.2.2 
Defining the Inverse of an Exponential Function 

6.2.3 
Investigating the Family of Logarithmic Functions 

6.2.4 
Transformations of Log Graphs 

6.2.5 
Investigating Compositions of Functions 
Closure 
6.CL 
Chapter Closure 
Chapter 7: 3D Graphing and Logarithms
Opening 
7.OP 
Chapter Opening 
Section 7.1 
7.1.1 
Creating a ThreeDimensional Model 

7.1.2 
Graphing Equations in Three Dimensions 

7.1.3 
Systems of ThreeVariable Equations 

7.1.4 
Solving Systems of Three Equations with Three Unknowns 

7.1.5 
Using Systems of Three Equations for Curve Fitting 
Section 7.2 
7.2.1 
Using Logarithms to Solve Exponential Equations 

7.2.2 
Investigating the Properties of Logarithms 

7.2.3 
Writing Equations of Exponential Functions 

7.2.4 
An Application of Logarithms 
Section 7.3 
7.3.1 
Introduction to Matrices 

7.3.2 
Matrix Multiplication 

7.3.3 
Matrix Multiplication with a Graphing Calculator 

7.3.4 
Writing Systems as Matrix Equations 

7.3.5 
Using Matrices to Solve Systems of Equations 
Closure 
7.CL 
Chapter Closure 
Chapter 8: Trigonometric Functions
Opening 
8.OP 
Chapter Opening 
Section 8.1 
8.1.1 
Introduction to Cyclic Models 

8.1.2 
Graphing the Sine Function 

8.1.3 
Unit Circle ↔ Graph 

8.1.4 
Graphing and Interpreting the Cosine Function 

8.1.5 
Defining a Radian 

8.1.6 
Building a Unit Circle 

8.1.7 
The Tangent Function 
Section 8.2 
8.2.1 
Transformations of y = sin x 

8.2.2 
One More Parameter for a Cyclic Function 

8.2.3 
Period of a Cyclic Function 

8.2.4 
Graph ↔ Equation 
Closure 
8.CL 
Chapter Closure 
Chapter 9: Polynomial Functions
Opening 
9.OP 
Chapter Opening 
Section 9.1 
9.1.1 
Sketching Graphs of Polynomial Functions 

9.1.2 
More Graphs of Polynomials 

9.1.3 
Stretch Coefficients for Polynomial Functions 
Section 9.2 
9.2.1 
Introducing Imaginary Numbers 

9.2.2 
Complex Roots 

9.2.3 
More Complex Numbers and Equations 
Section 9.3 
9.3.1 
Polynomial Division 

9.3.2 
Factors and Integral Roots 

9.3.3 
An Application of Polynomials 
Closure 
9.CL 
Chapter Closure 
Chapter 10: Probability and Counting
Opening 
10.OP 
Chapter Opening 
Section 10.1 
10.1.1 
Probability and Expected Value 

10.1.2 
Conditional Probabilities 
Section 10.2 
10.2.1 
The Fundamental Principle of Counting 

10.2.2 
Permutations 

10.2.3 
Combinations 

10.2.4 
Categorizing Counting Problems 

10.2.5 
Choosing Counting Methods 

10.2.6 
Some Challenging Probability Problems 
Closure 
10.CL 
Chapter Closure 
Chapter 11: Conic Sections
Opening 
11.OP 
Chapter Opening 
Section 11.1 
11.1.1 
A Special Property of Parabolas 

11.1.2 
Constructing and Analyzing Parabolas 
Section 11.2 
11.2.1 
Sections of a Cone 

11.2.2 
Multiple Perspective on Parabolas and Circles 

11.2.3 
Equations of Ellipses 

11.2.4 
Equation ↔ Graph for Ellipses 

11.2.5 
A New Conic Section 

11.2.6 
Equation ↔ Graph for Hyperbolas 
Section 11.3 
11.3.1 
Identifying and Graphing Conic Sections 

11.3.2 
Graphing Form for Conic Sections 

11.3.3 
Quadratic Relations 

11.3.4 
Conic Sections Project 
Closure 
11.CL 
Chapter Closure 
Chapter 12: Series
Chapter 12.1 
12.1.1 
Introduction to Arithmetic Series 

12.1.2 
More Arithmetic Series 

12.1.3 
General Arithmetic Series 

12.1.4 
Summation Notation and Combinations of Series 
Section 12.2 
12.2.1 
Mathematical Induction 
Section 12.3 
12.3.1 
Geometric Series 

12.3.2 
Infinite Series 
Section 12.4 
12.4.1 
Pascal’s Triangle and the Binomial Theorem 

12.4.2 
Applying the Binomial Theorem 
Section 12.5 
12.5.1 
The Number e 

12.5.2 
Calculating e and Using Natural Logarithms 
Closure 
12.CL 
Chapter Closure 
Chapter 13: Analytic Trigonometry
Chapter 13.1 
13.1.1 
Evaluating Trigonometric Equations 

13.1.2 
Solutions to Trigonometric Equations 

13.1.3 
Inverses of Trigonometric Functions 

13.1.4 
Reciprocal Trigonometric Functions 
Section 13.2 
13.2.1 
Trigonometric Identities 

13.2.2 
Proving Trigonometric Identities 

13.2.3 
Angle Sum and Difference Identities 
Closure 
13.CL 
Chapter Closure 
Checkpoint Materials:
Checkpoint 1: 
Using the SlopeIntercept Form of a Line to Solve a System of Equations 
Checkpoint 2: 
Solving Systems of Linear Equations in Two Variables 
Checkpoint 3: 
Multiplying Polynomials 
Checkpoint 4: 
Simplifying Expressions with Positive Exponents 
Checkpoint 5: 
Factoring Quadratic Expressions 
Checkpoint 6: 
Writing the Equation of a Line Given Two Points 
Checkpoint 7: 
Finding the x and yintercepts of a Quadratic Function 
Checkpoint 8: 
Finding the Slope of a Line through Two Points and the Distance Between the Points 
Checkpoint 9: 
Using Function Notation and Identifying the Domain and Range 
Checkpoint 10: 
Solving for One Variable in an Equation with Two or More Variables 
Checkpoint 11: 
Integral and Rational Exponents 
Checkpoint 12: 
Graphing Linear Inequalities 
Checkpoint 13: 
Solving Rational Equations 
Checkpoint 14: 
Completing the Square and Finding the Vertex for a Parabola 
Checkpoint 15: 
Writing and Solving Exponential Equations 
Checkpoint 16: 
Solving Absolute Value Equations and Inequalities 
Checkpoint 17: 
Finding an Equation for the Inverse of a Function 
Checkpoint 18: 
Solving a System of Equations in Three Variables 
Glossary
Index