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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: Transformations of Parents Graphs
Opening 
2.OP 
Chapter Opening 
Section 2.1 
2.1.1 
Modeling NonLinear Data 

2.1.2 
Parabola Investigation 

2.1.3 
Graphing a Parabola Without a Table 

2.1.4 
Rewriting in Graphing Form 

2.1.5 
Mathematical Modeling with Parabolas 
Section 2.2 
2.2.1 
Transforming Other Parent Graphs 

2.2.2 
Describing (h,k) for Each Family of Functions 

2.2.3 
Transformations of Functions 

2.2.4 
Transforming NonFunctions 

2.2.5 
Transforming PiecewiseDefined Functions 
Closure 
2.CL 
Chapter Closure 
Chapter 3: Equivalent Forms
Opening 
3.OP 
Chapter Opening 
Section 3.1 
3.1.1 
Expressions 

3.1.2 
Rewriting Expressions and Determining Equivalence 

3.1.3 
Soving by Rewriting 
Section 3.2 
3.2.1 
Investigating Rational Functions 

3.2.2 
Simplifying Rational Expressions 

3.2.3 
Multiplying and Dividing Rational Expressions 

3.2.4 
Adding and Subtracting Rational Expressions 

3.2.5 
Creating New Functions 
Closure 
3.CL 
Chapter Closure 
Chapter 4: Solving and Intersections
Opening 
4.OP 
Chapter Opening 
Section 4.1 
4.1.1 
Strategies for Solving Equations 

4.1.2 
Solving Equations and Systems Graphically 

4.1.3 
Finding Multiple Solutions to Systems of Equations 

4.1.4 
Using Systems of Equations to Solve Problems 
Section 4.2 
4.2.1 
Solving Inequalities with One or Two Variables 

4.2.2 
Using Systems to Solve a Problem 

4.2.3 
Application of Systems of Linear Inequalities 

4.2.4 
Using Graphing to Find Solutions 
Closure 
4.CL 
Chapter Closure 
Chapter 5: Inverses and Logarithms
Opening 
5.OP 
Chapter Opening 
Section 5.1 
5.1.1 
”Undo” Equations 

5.1.2 
Using a Graph to Find an Inverse 

5.1.3 
Finding Inverses and Justifying Algebraically 
Section 5.2 
5.2.1 
Finding the Inverse of an Exponential Function 

5.2.2 
Defining the Inverse of an Exponential Function 

5.2.3 
Investigating the Family of Logarithmic Functions 

5.2.4 
Transformations of Logarithmic Functions 

5.2.5 
Investigating Compositions of Functions 
Closure 
5.CL 
Chapter Closure 
Chapter 6: 3D Graphing and Logarithms
Opening 
6.OP 
Chapter Opening 
Section 6.1 
6.1.1 
Creating a ThreeDimensional Model 

6.1.2 
Graphing Equations in Three Dimensions 

6.1.3 
Systems of ThreeVariable Equations 

6.1.4 
Solving Systems of Three Equations with Three Unknowns 

6.1.5 
Using Systems of Three Equations for Curve Fitting 
Section 6.2 
6.2.1 
Using Logarithms to Solve Exponential Equations 

6.2.2 
Investigating the Properties of Logarithms 

6.2.3 
Writing Equations of Exponential Functions 

6.2.4 
An Application of Logarithms 
Closure 
6.CL 
Chapter Closure 
Chapter 7: Trigonometric Functions
Opening 
7.OP 
Chapter Opening 
Section 7.1 
7.1.1 
Introduction to Cyclic Models 

7.1.2 
Graphing the Sine Function 

7.1.3 
Unit Circle ↔ Graph 

7.1.4 
Graphing and Interpreting the Cosine Function 

7.1.5 
Defining a Radian 

7.1.6 
Building a Unit Circle 

7.1.7 
The Tangent Function 
Section 7.2 
7.2.1 
Transformation of y = sin x 

7.2.2 
One More Parameter for a Cyclic Function 

7.2.3 
Period of a Cyclic Function 

7.2.4 
Graph ↔ Equation 
Closure 
7.CL 
Chapter Closure 
Chapter 8: Polynomials
Opening 
8.OP 
Chapter Opening 
Section 8.1 
8.1.1 
Sketching Graphs of Polynomial Functions 

8.1.2 
More Graphs of Polynomials 

8.1.3 
Stretch Factor for Polynomial Functions 
Section 8.2 
8.2.1 
Introducing Imaginary Numbers 

8.2.2 
Complex Roots 

8.2.5 
More Complex Numbers and Equations 
Section 8.3 
8.3.1 
Polynomial Division 

8.3.2 
Factors and Integral Roots 

8.3.3 
An Application of Polynomials 
Closure 
8.CL 
Chapter Closure 
Chapter 9: Randomization and Normal Distributions
Opening 
9.OP 
Chapter Opening 
Section 9.1 
9.1.1 
Survey Design 

9.1.2 
Samples and the Role of Randomness 

9.1.3 
Bias in Convenience Samples 
Section 9.2 
9.2.1 
Testing Cause and Effect with Experiments 

9.2.2 
Conclusions From Studies 
Section 9.3 
9.3.1 
Relative Frequency Histograms 

9.3.2 
The Normal Probability Density Function 

9.3.3 
Percentiles 
Closure 
9.CL 
Chapter Closure 
Chapter 10: Series
Opening 
10.OP 
Chapter Opening 
Section 10.1 
10.1.1 
Introduction to Arithmetic Series 

10.1.2 
More Arithmetic Series 

10.1.3 
General Arithmetic Series 

10.1.4 
Summation Notation and Combinations of Series 
Section 10.2 
10.2.1 
Geometric Series 

10.2.2 
Infinite Series 
Section 10.3 
10.3.1 
Pascal’s Triangle and the Binomial Theorem 

10.3.2 
The Number e 
Closure 
10.CL 
Chapter Closure 
Chapter 11: Simulating Sampling Variability
Opening 
11.OP 
Chapter Opening 
Section 11.1 
11.1.1 
Simulations of Probability 

11.1.2 
More Simulations of Probability 

11.1.3 
Simulating Sampling Variability 
Section 11.2 
11.2.1 
Statistical Test Using Sampling Variability 

11.2.2 
Variability in Experimental Results 

11.2.3 
Quality Control 

11.2.4 
Statistical Process Control 
Section 11.3 
11.3.1 
Analyzing Decisions and Strategies 
Closure 
11.CL 
Chapter Closure 
Chapter 12: Analytic Trigonometry
Chapter 12.1 
12.1.1 
Analyzing Trigonometric Equations 

12.1.2 
Solutions to Trigonometric Equations 

12.1.3 
Inverses of Trigonometric Functions 

12.1.4 
Reciprocal Trigonometric Functions 
Section 12.2 
12.2.1 
Trigonometric Identities 

12.2.2 
Proving Trigonometric Identities 

12.2.3 
Angle Sum and Difference Identities 
Closure 
12.CL 
Chapter Closure 
Appendix A: Sequences
Section A.1 
A.1.1 
Representing Exponential Growth 

A.1.2 
Rebound Ratios 

A.1.3 
The Bouncing Ball and Exponential Decay 
Section A.2 
A.2.1 
Generating and Investigating Sequences 

A.2.2 
Generalizing Arithmetic Sequences 

A.2.3 
Recursive Sequences 
Section A.3 
A.3.1 
Patterns of Growth in Tables and Graphs 

A.3.2 
Using Multipliers to Solve Problems 

A.3.3 
Comparing Sequences to Functions 
Closure 
A.CL 
Chapter Closure 
Appendix B: Exponential Functions
Section B.1 
B.1.1 
Investigation y = b^{x} 

B.1.2 
Multiple Representations of Exponential Functions 

B.1.3 
More Applications of Exponential Growth 

B.1.4 
Exponential Decay 

B.1.5 
Graph → Equation 

B.1.6 
Completing the Multiple Representations Web 
Section B.2 
B.2.1 
Curve Fitting and Fractional Exponents 

B.2.2 
More Curve Fitting 

B.2.3 
Solving a System of Exponential Functions Graphically 
Closure 
B.CL 
Chapter Closure 
Appendix C: Comparing SingleVariable Data
Section C.1 
C.1.1 
Investigating Data Representations 

C.1.2 
Comparing Data 

C.1.3 
Standard Deviation 
Closure 
C.CL 
Chapter Closure 
Checkpoint Materials
CP 2A: 
Finding the Distance Between Two Points and the Equation of a Line 
CP 2B: 
Solving Linear Systems in Two Variables 
CP 3A: 
Expressions with Integral and Rational Exponents 
CP 3B: 
Using Function Notation and Identifying Domain and Range 
CP 4A: 
Writing Equations for Arithmetic and Geometric Sequences 
CP 4B: 
Solving for One Variable in an Equation with Two or More Variables 
CP 5A: 
Multiplying Polynomials 
CP 5B: 
Factoring Quadratics 
CP 6A: 
Multiplying and Dividing Rational Expressions 
CP 6B: 
Adding and Subtracting Rational Expressions 
CP 7A: 
Finding the x and yintercepts of a Quadratic Function 
CP 7B: 
Completing the Square to Find the Vertex of a Parabola 
CP 8A: 
Solving and Graphing Inequalities 
CP 8B: 
Multiplying Polynomials 
CP 9A: 
Writing and Solving Exponential Equations 
CP 9B: 
Finding the Equation for the Inverse of a Function 
CP 10: 
Rewriting Expressions and Solving Equations with Logarithms 
CP 11: 
Solving Rational Equations 
Glossary
Index