Chapter 1: Graphs

Section
 Topic

1.1  The
Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing
Equations 
1.2
 Intercepts;
Symmetry Graphing Key Equations 1.2.51 Intercepts and Symmetry 
1.3  Solving Equations
Using a Graphing Utility 
1.4  Lines 1.4.66 Lines 1.4.124 Lines 
1.5  Circles 1.5.26 Circles 

Chapter 2: Functions and Their
Graphs

Section
 Topic

2.1  Functions 
2.2  The Graph
of a Function 
2.3  Properties
of Functions 2.3.58 Properties of Functions 2.3.76 Properties of Functions 
2.4  Library of
Functions; Piecewisedefined Functions 2.4.56 Piecewise Function 
2.5  Graphing
Techniques: Transformations 
2.6  Mathematical
Models: Building Functions 2.6.8 Building Functions 2.6.22 Building Functions 

Chapter 3: Linear and Quadratic
Functions

Section  Topic 
3.1  Linear
Functions and Their Properties 
3.2  Linear
Models: Building Linear Functions from Data 
3.3  Quadratic
Functions and Their Properties 3.3.92 Quadratic Functions and Their Properties 
3.4  Build
Quadratic Models from Verbal Descriptions and from Data 3.4.6 Build Quadratic Models 
3.5  Inequalities
Involving Quadratic Functions 

Chapter 4: Polynomial and
Rational Functions

Section  Topic 
4.1  Polynomial
Functions and Models 4.1.78 Polynomial Function 4.1.90 Polynomial Function 
4.2  The Real
Zeros of a Polynomial Function 4.2.76 Intermediate Value Theorem 
4.3  Complex
Zeros; Fundamental Theorem of Algebra 4.3.20 Function from Zeros 4.3.28 Zeros from Function 
4.4  Properties
of Rational Functions 4.4.22+24 Domain of a Rational Function 4.4.38 Graph of a Rational Function 4.4.52+54 Asymptotes of a Rational Function 
4.5  The Graph
of a Rational Function 4.5.52 Rational Function Model 4.5.56 Rational Function Model 
4.6  Polynomial
and Rational Inequalities 4.6.36 Rational Inequality 4.6.44 Rational Inequality 

Chapter 5: Exponential and
Logarithmic Functions

Section  Topic 
5.1  Composite
Functions 5.1.36 Composite Functions Domain & Formula 5.1.44 Composite Functions Domain & Formula 5.1.70 Composite Function Model 
5.2  OnetoOne
Functions; Inverse Functions 5.2.56 Inverse Function 5.2.96 Inverse Function Model

5.3  Exponential
Functions 5.3.114 Exponential Function Model

5.4  Logarithmic
Functions 5.4.76 Logartihmic Function with Transformations 5.4.126 Logarithmic Function Model 
5.5  Properties
of Logarithms 
5.6  Logarithmic
and Exponential Equations 5.6.54 Solve Exponential Equation 5.6.100 Exponential Function Model 
5.7  Financial
Models 
5.8  Exponential
Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models 5.8.18 Exponential Decay Model 5.8.24 Logistic Growth 
5.9  Building
Exponential, Logarithmic, and Logistic Models from Data


Chapter 6: Trigonometric
Functions

Section
 Topic

6.1  Angles and
Their Measure 6.1.82+84 Angles and Arc Length Formula 6.1.102 Distance Between Cities 
6.2  Trigonometric
Functions: Unit Circle Approach 6.2.128 Trig Function Model 
6.3  Properties
of Trigonometric Functions 6.3.56 Values of Six Trig Functions 6.3.58 Values of Six Trig Functions 
6.4  Graphs of
the Sine and Cosine Functions 6.4.58 Graph of Sine Function 
6.5  Graphs of
the Tangent, Cotangent, Cosecant, and Secant Functions 6.5.40 Graph of Secant Function 
6.6  Phase
Shift; Sinusoidal Curve Fitting 6.6.14 Graph of Sinusoidal Function with Transformations 6.6.36 Sinusoidal Function Model

 
Chapter 7: Analytic
Trigonometry

Section
 Topic

7.1  The
Inverse Sine, Cosine, and Tangent Functions 7.1.68 Inverse Trig Function Equation 
7.2  The
Inverse Trigonometric Functions (Continued) 7.2.26+34 Composition of Trig and Inverse Trig Functions 
7.3  Trigonometric
Equations 7.3.34 Trigonometric Equation 7.3.68 Trigonometric Equation 7.3.80 Trigonometric Equation 7.3.86 Trigonometric Equation 
7.4  Trigonometric
Identities 7.4.48 Trigonometric Identities 7.4.84 Trigonometric Identities 
7.5  Sum and
Difference Formulas 7.5.62 Sum and Difference Formulas 7.5.78 Sum and Difference Formulas 
7.6  Doubleangle
and Halfangle Formulas 7.6.14 Doubleangle and Halfangle Formulas 
7.7  ProducttoSum
and SumtoProduct Formulas 
 
Chapter 8: Applications of
Trigonometric Functions

Section
 Topic

8.1  Right
Triangle Trigonometry; Applications 8.1.64 Right Triangle Trigonometry; Applications 8.1.74 Right Triangle Trigonometry; Applications 
8.2  The Law of
Sines 
8.3  The Law of
Cosines 
8.4  Area of a
Triangle 
8.5  Simple
Harmonic Motion; Damped Motion; Combining Waves 
 
Chapter 9: Polar Coordinates;
Vectors

Section
 Topic

9.1  Polar
Coordinates 9.1.38 Polar Coordinates 9.1.68 Polar Coordinates 9.1.82 Polar Coordinates 
9.2  Polar
Equations and Graphs 9.2.50 Polar Equations and Graphs 9.2.54 Polar Equations and Graphs 
9.3  The Complex
Plane; De Moivre’s Theorem 
9.4  Vectors 
9.5  The Dot
Product 
9.6  Vectors in
Space 
9.7  The Cross
Product 

Chapter 10: Analytic Geometry

Section  Topic 
10.1  Conics 
10.2  The
Parabola 
10.3  The
Ellipse 
10.4  The
Hyperbola 
10.5  Rotation
of Axes; General Form of a Conic 
10.6  Polar
Equations of Conics 
10.7  Plane
Curves and Parametric Equations 

Chapter 11: Systems of
Equations and Inequalities

Section
 Topic

11.1  Systems of
Linear Equations: Substitution and Elimination 
11.2  Systems of
Linear Equations: Matrices 
11.3  Systems of
Linear Equations: Determinants 
11.4  Matrix
Algebra 
11.5  Partial
Fraction Decomposition 
11.6  Systems of
Nonlinear Equations 
11.7  Systems of
Inequalities 
11.8  Linear
Programming 

Chapter 12: Sequences;
Induction; the Binomial Theorem

Section
 Topic

12.1  Sequences 
12.2  Arithmetic
Sequences 
12.3  Geometric
Sequences; Geometric Series 
12.4  Mathematical
Induction 
12.5  The
Binomial Theorem 

Chapter 13: Counting and
Probability

Section
 Topic

13.1  Counting 
13.2  Permutations
and Combinations 
13.3  Probability 

Chapter 14: A Preview of Calculus:
The Limit, Derivative, and Integral of a Function

Section  Topic 
14.1  Finding
Limits Using Tables and Graphs 
14.2  Algebra
Techniques for Finding Limits 
14.3  OneSided
Limits; Continuous Functions 
14.4  The Tangent
Problem; The Derivative 
14.5  The Area
Problem; The Integral 