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; Piecewise-defined 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 | One-to-One
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 | Double-angle
and Half-angle Formulas 7.6.14 Double-angle and Half-angle Formulas |
7.7 | Product-to-Sum
and Sum-to-Product 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 | One-Sided
Limits; Continuous Functions |
14.4 | The Tangent
Problem; The Derivative |
14.5 | The Area
Problem; The Integral |
