# Lesson 2 Homework Practice Sequences As Functions

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**Chapter 1: Investigations and Functions**

Opening | dfknj.wz.cz | Chapter Opening |

Section | Solving Puzzles in Teams | |

Using a Graphing Calculator to Explore a Function | ||

Domain and Range | ||

Points of Intersection in Multiple Representations | ||

Section | Modeling a Geometric Relationship | |

Function Investigation | ||

The Family of Linear Functions | ||

Function Investigation Challenge | ||

Closure | dfknj.wz.cz | Chapter Closure |

**Chapter 2: Sequences and Equivalence**

Opening | dfknj.wz.cz | Chapter Opening |

Section | Representing Exponential Growth | |

Rebound Ratio | ||

The Bouncing Ball and Exponential Decay | ||

Generating and Investigating Sequences | ||

Generalizing Arithmetic Sequences | ||

Using Multipliers to Solve Problems | ||

Comparing Sequences and Functions | ||

Sequences that Begin with n = 1 | ||

Section | Equivalent Expressions | |

Area Models and Equivalent Expressions | ||

Solving by Rewriting | ||

Closure | dfknj.wz.cz | Chapter Closure |

**Chapter 3: Exponential Functions**

Opening | dfknj.wz.cz | Chapter Opening |

Section | Investigating y = b^{x} | |

Multiple Representations | ||

More Applications of Exponential Growth | ||

Exponential Decay | ||

Graph to Rule | ||

Completing the Web | ||

Section | Curve Fitting and Fractional Exponents | |

More Curve Fitting | ||

Solving a System of Exponential Functions Graphically | ||

Closure | dfknj.wz.cz | Chapter Closure |

**Chapter 4: Transformations of Parent Graphs**

Opening | dfknj.wz.cz | Chapter Opening |

Section | Modeling Non-Linear Data | |

Parabola Investigation | ||

Graphing a Parabola Without a Table | ||

Mathematical Modeling with Parabolas | ||

Section | Transforming Other Parent Graphs | |

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

Transforming the Absolute Value Parent Graph | ||

Transforming Non-Functions | ||

Section | Completing the Square | |

More Completing the Square | ||

Closure | dfknj.wz.cz | Chapter Closure |

**Chapter 5: Solving and Intersections**

Opening | dfknj.wz.cz | Chapter Opening |

Section | Strategies for Solving Equations | |

Solving Equations and Systems Graphically | ||

Finding Multiple Solutions to Systems of Equations | ||

Using Systems of Equations to Solve Problems | ||

Section | Solving Inequalities with One or Two Variables | |

Using Systems to Solve a Problem | ||

Applications of Systems of Linear Inequalities | ||

Using Graphs to Find Solutions | ||

Closure | dfknj.wz.cz | Chapter Closure |

**Chapter 6: Inverses and Logarithms**

Opening | dfknj.wz.cz | Chapter Opening |

Section | Undo Rules | |

Using a Graph to Find the Inverse | ||

Finding Inverses and Justifying Algebraically | ||

Section | Finding the Inverse of an Exponential Function | |

Defining the Inverse of an Exponential Function | ||

Investigating the Family of Logarithmic Functions | ||

Transformations of Log Graphs | ||

Investigating Compositions of Functions | ||

Closure | dfknj.wz.cz | Chapter Closure |

**Chapter 7: 3-D Graphing and Logarithms**

Opening | dfknj.wz.cz | Chapter Opening |

Section | Creating a Three-Dimensional Model | |

Graphing Equations in Three Dimensions | ||

Systems of Three-Variable Equations | ||

Solving Systems of Three Equations with Three Unknowns | ||

Using Systems of Three Equations for Curve Fitting | ||

Section | Using Logarithms to Solve Exponential Equations | |

Investigating the Properties of Logarithms | ||

Writing Equations of Exponential Functions | ||

An Application of Logarithms | ||

Section | Introduction to Matrices | |

Matrix Multiplication | ||

Matrix Multiplication with a Graphing Calculator | ||

Writing Systems as Matrix Equations | ||

Using Matrices to Solve Systems of Equations | ||

Closure | dfknj.wz.cz | Chapter Closure |

**Chapter 8: Trigonometric Functions**

Opening | dfknj.wz.cz | Chapter Opening |

Section | Introduction to Cyclic Models | |

Graphing the Sine Function | ||

Unit Circle ↔ Graph | ||

Graphing and Interpreting the Cosine Function | ||

Defining a Radian | ||

Building a Unit Circle | ||

The Tangent Function | ||

Section | Transformations of y = sin x | |

One More Parameter for a Cyclic Function | ||

Period of a Cyclic Function | ||

Graph ↔ Equation | ||

Closure | dfknj.wz.cz | Chapter Closure |

**Chapter 9: Polynomial Functions**

Opening | dfknj.wz.cz | Chapter Opening |

Section | Sketching Graphs of Polynomial Functions | |

More Graphs of Polynomials | ||

Stretch Coefficients for Polynomial Functions | ||

Section | Introducing Imaginary Numbers | |

Complex Roots | ||

More Complex Numbers and Equations | ||

Section | Polynomial Division | |

Factors and Integral Roots | ||

An Application of Polynomials | ||

Closure | dfknj.wz.cz | Chapter Closure |

**Chapter Probability and Counting**

Opening | OP | Chapter Opening |

Section | Probability and Expected Value | |

Conditional Probabilities | ||

Section | The Fundamental Principle of Counting | |

Permutations | ||

Combinations | ||

Categorizing Counting Problems | ||

Choosing Counting Methods | ||

Some Challenging Probability Problems | ||

Closure | CL | Chapter Closure |

**Chapter Conic Sections**

Opening | OP | Chapter Opening |

Section | A Special Property of Parabolas | |

Constructing and Analyzing Parabolas | ||

Section | Sections of a Cone | |

Multiple Perspective on Parabolas and Circles | ||

Equations of Ellipses | ||

Equation ↔ Graph for Ellipses | ||

A New Conic Section | ||

Equation ↔ Graph for Hyperbolas | ||

Section | Identifying and Graphing Conic Sections | |

Graphing Form for Conic Sections | ||

Quadratic Relations | ||

Conic Sections Project | ||

Closure | CL | Chapter Closure |

**Chapter Series**

Chapter | Introduction to Arithmetic Series | |

More Arithmetic Series | ||

General Arithmetic Series | ||

Summation Notation and Combinations of Series | ||

Section | Mathematical Induction | |

Section | Geometric Series | |

Infinite Series | ||

Section | Pascal’s Triangle and the Binomial Theorem | |

Applying the Binomial Theorem | ||

Section | The Number e | |

Calculating e and Using Natural Logarithms | ||

Closure | CL | Chapter Closure |

**Chapter Analytic Trigonometry**

Chapter | Evaluating Trigonometric Equations | |

Solutions to Trigonometric Equations | ||

Inverses of Trigonometric Functions | ||

Reciprocal Trigonometric Functions | ||

Section | Trigonometric Identities | |

Proving Trigonometric Identities | ||

Angle Sum and Difference Identities | ||

Closure | CL | Chapter Closure |

**Checkpoint Materials:**

Checkpoint 1: | Using the Slope-Intercept 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 y-intercepts 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 | Solving for One Variable in an Equation with Two or More Variables |

Checkpoint | Integral and Rational Exponents |

Checkpoint | Graphing Linear Inequalities |

Checkpoint | Solving Rational Equations |

Checkpoint | Completing the Square and Finding the Vertex for a Parabola |

Checkpoint | Writing and Solving Exponential Equations |

Checkpoint | Solving Absolute Value Equations and Inequalities |

Checkpoint | Finding an Equation for the Inverse of a Function |

Checkpoint | Solving a System of Equations in Three Variables |

**Glossary****Index**### Chapter 1

Chapter 1

Expressions and Formulas | Skills Practice | p.1 | |

Practice | p.2 | ||

Properties of Real Numbers | Skills Practice | p.3 | |

Practice | p.4 | ||

Solving Equations | Skills Practice | p.5 | |

Practice | p.6 | ||

Solving Absolute Value Equations | Skills Practice | p.7 | |

Practice | p.8 | ||

Solving Inequalities | Skills Practice | p.9 | |

Practice | p | ||

Solving Compound and Absolute Value Inequalities | Skills Practice | p | |

Practice | p |

### Chapter 2

Chapter 2

Relations and Functions | Skills Practice | p | |

Practice | p | ||

Linear Relations and Functions | Skills Practice | p | |

Practice | p | ||

Rate of Change and Slope | Skills Practice | p | |

Practice | p | ||

Writing Linear Equations | Skills Practice | p | |

Practice | p | ||

Scatter Plots and Lines of Regressions | Skills Practice | p | |

Practice | p | ||

Special Functions | Skills Practice | p | |

Practice | p | ||

Parent Functions and Transformations | Skills Practice | p | |

Practice | p | ||

Graphing Linear Absolute Value Inequalities | Skills Practice | p | |

Practice | p |

### Chapter 3

Chapter 3

Solving Systems of Equations by Graphing | Skills Practice | p | |

Practice | p | ||

Solving Systems of Equations Algebraically | Skills Practice | p | |

Practice | p | ||

Solving Systems of Inequalities by Graphing | Skills Practice | p | |

Practice | p | ||

Optimization with Linear Programming | Skills Practice | p | |

Practice | p | ||

Systems of Equations in Three Variables | Skills Practice | p | |

Practice | p |

### Chapter 4

Chapter 4

Introduction to Matrices | Skills Practice | p | |

Practice | p | ||

Operations with Matrices | Skills Practice | p | |

Practice | p | ||

Multiplying Matrices | Skills Practice | p | |

Practice | p | ||

Transformations with Matrices | Skills Practice | p | |

Practice | p | ||

Determinants and Cramer's Rule | Skills Practice | p | |

Practice | p | ||

Inverse Matrices and Systems of Equations | Skills Practice | p | |

Practice | p |

### Chapter 5

Chapter 5

Graphing Quadratic Equations | Skills Practice | p | |

Practice | p | ||

Solving Quadratic Equations by Graphing | Skills Practice | p | |

Practice | p | ||

Solving Quadratic Equations by Factoring | Skills Practice | p | |

Practice | p | ||

Complex Numbers | Skills Practice | p | |

Practice | p | ||

Completing the Square | Skills Practice | p | |

Practice | p | ||

The Quadratic Formula and the Discriminant | Skills Practice | p | |

Practice | p | ||

Transformations with Quadratic Functions | Skills Practice | p | |

Practice | p | ||

Quadratic Inequalities | Skills Practice | p | |

Practice | p |

### Chapter 6

Chapter 6

Operations with Polynomials | Skills Practice | p | |

Practice | p | ||

Dividing Polynomials | Skills Practice | p | |

Practice | p | ||

Polynomial Functions | Skills Practice | p | |

Practice | p | ||

Analyzing Graphs of Polynomial Functions | Skills Practice | p | |

Practice | p | ||

Solving Polynomial Equations | Skills Practice | p | |

Practice | p | ||

The Remainder and Factor Theorems | Skills Practice | p | |

Practice | p | ||

Roots and Zeros | Skills Practice | p | |

Practice | p | ||

Rational Zero Theorem | Skills Practice | p | |

Practice | p |

### Chapter 7

Chapter 7

Operations on Functions | Skills Practice | p | |

Practice | p | ||

Inverse Functions and Relations | Skills Practice | p | |

Practice | p | ||

Square Root Functions and Inequalities | Skills Practice | p | |

Practice | p | ||

nth Roots | Skills Practice | p | |

Practice | p | ||

Operations with Radical Expressions | Skills Practice | p | |

Practice | p | ||

Rational Exponents | Skills Practice | p | |

Practice | p | ||

Solving Radical Equations and Inequalities | Skills Practice | p | |

Practice | p |

### Chapter 8

Chapter 8

Graphing Exponential Functions | Skills Practice | p | |

Practice | p | ||

Solving Exponential Equations and Inequalities | Skills Practice | p | |

Practice | p | ||

Logarithms and Logarithmic Functions | Skills Practice | p | |

Practice | p | ||

Solving Logarithmic Equations and Inequalities | Skills Practice | p | |

Practice | p | ||

Properties of Logarithms | Skills Practice | p | |

Practice | p | ||

Common Logarithms | Skills Practice | p | |

Practice | p | ||

Base e and Natural Logarithms | Skills Practice | p | |

Practice | p | ||

Using Exponential and Logarithmic Functions | Skills Practice | p | |

Practice | p |

### Chapter 9

Chapter 9

Multiplying and Dividing Rational Expressions | Skills Practice | p | |

Practice | p | ||

Adding and Subtracting Rational Expressions | Skills Practice | p | |

Practice | p | ||

Graphing Reciprocal Functions | Skills Practice | p | |

Practice | p | ||

Graphing Rational Functions | Skills Practice | p | |

Practice | p | ||

Variation Functions | Skills Practice | p | |

Practice | p | ||

Solving Rational Equations and Inequalities | Skills Practice | p | |

Practice | p |

### Chapter 10

Chapter 10

Midpoint and Distance Formulas | Skills Practice | p | |

Practice | p | ||

Parabolas | Skills Practice | p | |

Practice | p | ||

Circles | Skills Practice | p | |

Practice | p | ||

Ellipses | Skills Practice | p | |

Practice | p | ||

Hyperbolas | Skills Practice | p | |

Practice | p | ||

Identifying Conic Sections | Skills Practice | p | |

Practice | p | ||

Solving Quadratic Systems | Skills Practice | p | |

Practice | p |

### Chapter 11

Chapter 11

Sequences as Functions | Skills Practice | p | |

Practice | p | ||

Arithmetic Sequences and Series | Skills Practice | p | |

Practice | p | ||

Geometric Sequences and Series | Skills Practice | p | |

Practice | p | ||

Infinite Geometric Series | Skills Practice | p | |

Practice | p | ||

Recursion and Iteration | Skills Practice | p | |

Practice | p | ||

The Binomial Theorem | Skills Practice | p | |

Practice | p | ||

Proof by Mathematical Induction | Skills Practice | p | |

Practice | p |

### Chapter 12

Chapter 12

Experiments, Surveys, and Observational Studies | Skills Practice | p | |

Practice | p | ||

Statistical Analysis | Skills Practice | p | |

Practice | p | ||

Conditional Probability | Skills Practice | p | |

Practice | p | ||

Probability Distributions | Skills Practice | p | |

Practice | p | ||

The Normal Distribution | Skills Practice | p | |

Practice | p | ||

Hypothesis Testing | Skills Practice | p | |

Practice | p | ||

Binomial Distributions | Skills Practice | p | |

Practice | p |

### Chapter 13

Chapter 13

Trigonometric Functions in Right Triangles | Skills Practice | p | |

Practice | p | ||

Angles and Angle Measure | Skills Practice | p | |

Practice | p | ||

Trigonometric Functions of General Angles | Skills Practice | p | |

Practice | p | ||

Law of Sines | Skills Practice | p | |

Practice | p | ||

Law of Cosines | Skills Practice | p | |

Practice | p | ||

Circular Functions | Skills Practice | p | |

Practice | p | ||

Graphing Trigonometric Functions | Skills Practice | p | |

Practice | p | ||

Translations of Trigonometric Graphs | Skills Practice | p | |

Practice | p | ||

Inverse Trigonometric Functions | Skills Practice | p | |

Practice | p |

### Chapter 14

Chapter 14

Trigonometric Identities | Skills Practice | p | |

Practice | p | ||

Verifying Trigonometric Identities | Skills Practice | p | |

Practice | p | ||

Sum and Difference of Angles Formulas | Skills Practice | p | |

Practice | p | ||

Double-Angle and Half-Angle Formulas | Skills Practice | p | |

Practice | p | ||

Solving Trigonometric Equations | Skills Practice | p | |

Practice | p |