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Lesson 2 Homework Practice Sequences As Functions

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Chapter 1: Investigations and Functions

Openingdfknj.wz.czChapter 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
Closuredfknj.wz.czChapter Closure

Chapter 2: Sequences and Equivalence

Openingdfknj.wz.czChapter 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
Closuredfknj.wz.czChapter Closure

Chapter 3: Exponential Functions

Openingdfknj.wz.czChapter Opening
Section Investigating y = bx
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
Closuredfknj.wz.czChapter Closure

Chapter 4: Transformations of Parent Graphs

Openingdfknj.wz.czChapter 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
Closuredfknj.wz.czChapter Closure

Chapter 5: Solving and Intersections

Openingdfknj.wz.czChapter 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
Closuredfknj.wz.czChapter Closure

Chapter 6: Inverses and Logarithms

Openingdfknj.wz.czChapter 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
Closuredfknj.wz.czChapter Closure

Chapter 7: 3-D Graphing and Logarithms

Openingdfknj.wz.czChapter 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
Closuredfknj.wz.czChapter Closure

Chapter 8: Trigonometric Functions

Openingdfknj.wz.czChapter 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
Closuredfknj.wz.czChapter Closure

Chapter 9: Polynomial Functions

Openingdfknj.wz.czChapter 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
Closuredfknj.wz.czChapter Closure

Chapter Probability and Counting

OpeningOPChapter 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
ClosureCLChapter Closure

Chapter Conic Sections

OpeningOPChapter 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
ClosureCLChapter 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
ClosureCLChapter 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
ClosureCLChapter 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 FormulasSkills Practicep.1
Practicep.2
Properties of Real NumbersSkills Practicep.3
Practicep.4
Solving EquationsSkills Practicep.5
Practicep.6
Solving Absolute Value EquationsSkills Practicep.7
Practicep.8
Solving InequalitiesSkills Practicep.9
Practicep
Solving Compound and Absolute Value InequalitiesSkills Practicep
Practicep

Chapter 2

Chapter 2

Relations and FunctionsSkills Practicep
Practicep
Linear Relations and FunctionsSkills Practicep
Practicep
Rate of Change and SlopeSkills Practicep
Practicep
Writing Linear EquationsSkills Practicep
Practicep
Scatter Plots and Lines of RegressionsSkills Practicep
Practicep
Special FunctionsSkills Practicep
Practicep
Parent Functions and TransformationsSkills Practicep
Practicep
Graphing Linear Absolute Value InequalitiesSkills Practicep
Practicep

Chapter 3

Chapter 3

Solving Systems of Equations by GraphingSkills Practicep
Practicep
Solving Systems of Equations AlgebraicallySkills Practicep
Practicep
Solving Systems of Inequalities by GraphingSkills Practicep
Practicep
Optimization with Linear ProgrammingSkills Practicep
Practicep
Systems of Equations in Three VariablesSkills Practicep
Practicep

Chapter 4

Chapter 4

Introduction to MatricesSkills Practicep
Practicep
Operations with MatricesSkills Practicep
Practicep
Multiplying MatricesSkills Practicep
Practicep
Transformations with MatricesSkills Practicep
Practicep
Determinants and Cramer's RuleSkills Practicep
Practicep
Inverse Matrices and Systems of EquationsSkills Practicep
Practicep

Chapter 5

Chapter 5

Graphing Quadratic EquationsSkills Practicep
Practicep
Solving Quadratic Equations by GraphingSkills Practicep
Practicep
Solving Quadratic Equations by FactoringSkills Practicep
Practicep
Complex NumbersSkills Practicep
Practicep
Completing the SquareSkills Practicep
Practicep
The Quadratic Formula and the DiscriminantSkills Practicep
Practicep
Transformations with Quadratic FunctionsSkills Practicep
Practicep
Quadratic InequalitiesSkills Practicep
Practicep

Chapter 6

Chapter 6

Operations with PolynomialsSkills Practicep
Practicep
Dividing PolynomialsSkills Practicep
Practicep
Polynomial FunctionsSkills Practicep
Practicep
Analyzing Graphs of Polynomial FunctionsSkills Practicep
Practicep
Solving Polynomial EquationsSkills Practicep
Practicep
The Remainder and Factor TheoremsSkills Practicep
Practicep
Roots and ZerosSkills Practicep
Practicep
Rational Zero TheoremSkills Practicep
Practicep

Chapter 7

Chapter 7

Operations on FunctionsSkills Practicep
Practicep
Inverse Functions and RelationsSkills Practicep
Practicep
Square Root Functions and InequalitiesSkills Practicep
Practicep
nth RootsSkills Practicep
Practicep
Operations with Radical ExpressionsSkills Practicep
Practicep
Rational ExponentsSkills Practicep
Practicep
Solving Radical Equations and InequalitiesSkills Practicep
Practicep

Chapter 8

Chapter 8

Graphing Exponential FunctionsSkills Practicep
Practicep
Solving Exponential Equations and InequalitiesSkills Practicep
Practicep
Logarithms and Logarithmic FunctionsSkills Practicep
Practicep
Solving Logarithmic Equations and InequalitiesSkills Practicep
Practicep
Properties of LogarithmsSkills Practicep
Practicep
Common LogarithmsSkills Practicep
Practicep
Base e and Natural LogarithmsSkills Practicep
Practicep
Using Exponential and Logarithmic FunctionsSkills Practicep
Practicep

Chapter 9

Chapter 9

Multiplying and Dividing Rational ExpressionsSkills Practicep
Practicep
Adding and Subtracting Rational ExpressionsSkills Practicep
Practicep
Graphing Reciprocal FunctionsSkills Practicep
Practicep
Graphing Rational FunctionsSkills Practicep
Practicep
Variation FunctionsSkills Practicep
Practicep
Solving Rational Equations and InequalitiesSkills Practicep
Practicep

Chapter 10

Chapter 10

Midpoint and Distance FormulasSkills Practicep
Practicep
ParabolasSkills Practicep
Practicep
CirclesSkills Practicep
Practicep
EllipsesSkills Practicep
Practicep
HyperbolasSkills Practicep
Practicep
Identifying Conic SectionsSkills Practicep
Practicep
Solving Quadratic SystemsSkills Practicep
Practicep

Chapter 11

Chapter 11

Sequences as FunctionsSkills Practicep
Practicep
Arithmetic Sequences and SeriesSkills Practicep
Practicep
Geometric Sequences and SeriesSkills Practicep
Practicep
Infinite Geometric SeriesSkills Practicep
Practicep
Recursion and IterationSkills Practicep
Practicep
The Binomial TheoremSkills Practicep
Practicep
Proof by Mathematical InductionSkills Practicep
Practicep

Chapter 12

Chapter 12

Experiments, Surveys, and Observational StudiesSkills Practicep
Practicep
Statistical AnalysisSkills Practicep
Practicep
Conditional ProbabilitySkills Practicep
Practicep
Probability DistributionsSkills Practicep
Practicep
The Normal DistributionSkills Practicep
Practicep
Hypothesis TestingSkills Practicep
Practicep
Binomial DistributionsSkills Practicep
Practicep

Chapter 13

Chapter 13

Trigonometric Functions in Right TrianglesSkills Practicep
Practicep
Angles and Angle MeasureSkills Practicep
Practicep
Trigonometric Functions of General AnglesSkills Practicep
Practicep
Law of SinesSkills Practicep
Practicep
Law of CosinesSkills Practicep
Practicep
Circular FunctionsSkills Practicep
Practicep
Graphing Trigonometric FunctionsSkills Practicep
Practicep
Translations of Trigonometric GraphsSkills Practicep
Practicep
Inverse Trigonometric FunctionsSkills Practicep
Practicep

Chapter 14

Chapter 14

Trigonometric IdentitiesSkills Practicep
Practicep
Verifying Trigonometric IdentitiesSkills Practicep
Practicep
Sum and Difference of Angles FormulasSkills Practicep
Practicep
Double-Angle and Half-Angle FormulasSkills Practicep
Practicep
Solving Trigonometric EquationsSkills Practicep
Practicep