Functions and Relations 11

Title page
Contents
Introduction
Chapter 1 Sequences and Series
Curriculum Expectations
Necessary Skills
1. Review: Percent
2. New: Exponent Laws for Integer Exponents
3. New: Numerical Roots
4. New: Patterns and Sequences
1.1 Linear Growth and Arithmetic Sequences
1.2 Exponential Growth and Geometric Sequences
1.3 The General Term of a Sequence
Self-Check 1.1–1.3 (Functions)
1.4 Recursion Formulas (Functions and Relations)
Self-Check 1.1–1.4 (Functions and Relations)
1.5 Defining Rational Exponents
1.6 Applying the Exponent Laws
Self-Check 1.5, 1.6
1.7 The Sum of an Arithmeticc Series
1.8 The Sum of a Geometric Series
Self-Check 1.7, 1.8
Insights into a Rich Problem: The Bouncing Ball
Review Exercises
Self-Test
Chapter 2 Rational Expressions
Curriculum Expectations
Necessary Skills
1. Review: Operations with Fractions
2. Review: Operations with Monomials
3. Review: Factoring Polynomials
2.1 Operations with Polynomials
2.2 Evaluating Rational Expressions
2.3 Simplifying Rational Expressions
Self-Check 2.1–2.3
2.4 Multiplying and Dividing Rational Expressions
2.5 Adding and Subtracting Rational Expressions: Part I
2.6 Adding and Subtracting Rational Expressions: Part II
Self-Check 2.4–2.6
Insights into a Rich Problem: How Much Time Does Extra Speed Save?
Review Exercises
Self-Test
Chapter 3 Financial Mathematics
Curriculum Expectations
Necessary Skills
1. New: Simple Interest
2. Review: Solving Equations
3. Review: Geometric Series
4. Review: Using a Calculator to Evaluate Expressions
3.1 Compound Interest: Amount and Present Value
3.2 Compound Interest: Other Compounding Periods
Self-Check 3.1, 3.2
3.3 The Amount of an Annuity
3.4 The Present Value of an Annuity
Self-Check 3.3, 3.4
3.5 Mortgages
3.6 Investigate: Using the TVM Solver on a Graphing Calculator
3.7 Amortization Tables
Self-Check 3.5–3.7
Insights into a Rich Problem: Where Did the $314 Come From?
Review Exercises
Self-Test
Chapter 4 Quadratic Functions and Complex Numbers
Curriculum Expectations
Necessary Skills
1. Review: The Quadratic Function y=ax2+bx+c
2. Review: Number Systems
3. Review: Intercepts and Zeros
4. New: Multiplying and Dividing Radicals
4.1 Maximum or Minimum Value of a Quadratic Function
4.2 Solving Quadratic Equations
Self-Check 4.1, 4.2
4.3 Introduction to Complex Numbers
4.4 Operations with Complex Numbers (Functions and Relations)
Self-Check 4.3, 4.4
Insights into a Rich Problem: Parabolas and Lines
Review Exercises
Self-Test
Chapter 5 Trigonometric Functions
Curriculum Expectations
Necessary Skills
1. Review: Trigonometric Ratios in Right Triangles
2. Review: The Sine Law in Acute Triangles
3. Review: The Cosine Law in Acute Triangles
5.1 The Sine and Cosine of an Obtuse Angle
5.2 The Cosine Law and Sine Law in Obtuse Triangles
Self-Check 5.1, 5.2
5.3 Angles in Standard Position
5.4 Trigonometric Functions of Angles in Standard Position
5.5 Sine, Cosine, and Tangent of Special Angles
Self Check 5.3–5.5
5.6 Radian Measure
5.7 Trigonometric Functions of Angles in Radians
5.8 Trigonometric Equations
5.9 Trigonometric Identities
Self-Check 5.6–5.9
Insights into a Rich Problem: The 2-3-4 Triangle
Review Exercises
Self-Test
Chapter 6 Graphing Trigonometric Functions
Curriculum Expectations
Necessary Skills
1. Review: Transformations of Quadratic Functions
2. New: The Domain and Range of a Function
3. New: Independent and Dependent Variables
4. New: Absolute Value
6.1 Introduction to Periodic Functions
6.2 The Sine and Cosine Functions
6.3 Graphing Sinusoidal Functions: Part I
Self-Check 6.1–6.3
6.4 Graphing Sinusoidal Functions: Part II
6.5 Applications of Sinusoidal Functions
6.6 Graphing the Tangent Function
Self-Check 6.4–6.6
Insights into a Rich Problem: The Equation of a Damped Spring
Review Exercises
Self-Test
Chapter 7 Transformations of Functions
Curriculum Expectations
Necessary Skills
1. New: The Vertical Line Test
2. New: Solving Linear Inequalities
7.1 Some Functions and Their Graphs
7.2 Function Notation
Self-Check NS, 7.1, 7.2
7.3 Transforming Functions
7.4 Combining Transformations of Functions
7.5 The Inverse of a Function
Self-Check 7.3–7.5
Insights into a Rich Problem: Inverting a Quartic Function
Review Exercises
Self-Test
Cumulative Review
Chapter 8 Loci: From Geometry to Algebra (Functions and Relations)
Curriculum Expectations
Necessary Skills
1. New: What Is a Relation?
2. Review: Geometry Properties
3. Review: Distance between Two Points
4. New: Squaring Expressions Containing Radicals
5. Review: Using The Geometer's Sketchpad
8.1 Locus
8.2 The Ellipse
Self-Check 8.1, 8.2
8.3 The Hyperbola
8.4 The Parabola
Self-Check 8.3, 8.4
8.5 Relating the Ellipse, Hyperbola, and Parabola
Insights into a Rich Problem: Finding the Ghost–The Reflection Property of an Ellipse
Review Exercises
Self-Test
Chapter 9 Conics: From Algebra to Geometry (Functions and Relations)
Curriculum Expectations
Necessary Skills
1. Review: The Quadratic Formula
2. New: Standard Equation of a Circle
3. Review: Solving a Linear System
9.1 Intersection of Lines and Circles
9.2 The Ellipse
Self-Check NS, 9.1, 9.2
9.3 The Hyperbola
9.4 The Parabola
Self-Check 9.3, 9.4
9.5 Applications of Quadratic Relations
9.6 The General Equation of a Conic
Self-Check 9.5, 9.6
Insights into a Rich Problem: The Reflection Property of a Parabola
Review Exercises
Self-Test
Answers
Glossary
Index
Acknowledgments