 ## Functions Strands and Subgroups in the Grade 11 Course

• A. CHARACTERISTICS OF FUNCTION
- Representing Functions
- Solving Problems Involving Quadratic Functions
- Determining Equivalent Algebraic Expressions
• B. EXPONENTIAL FUNCTIONS
- Representing Exponential Functions
- Connecting Graphs and Equations of Exponential Functions
- Solving Problems Involving Exponential Functions
• C. DISCRETE FUNCTIONS
- Representing Sequences
- Investigating Arithmetic and Geometric Sequences and Series
- Solving Problems Involving Financial Applications
• D. TRIGONOMETRIC FUNCTIONS
- Determining and Applying Trigonometric Ratios
- Connecting Graphs and Equations of Sinusoidal Functions
- Solving Problems Involving Sinusoidal Functions

### Chapter 1: Introduction to Functions

1.1: Relations and Functions
Curious Math
1.2: Function Notation
1.3: Exploring Properties of Parent Functions
1.4: Determining the Domain and Range of a Function
1.5: The Inverse Function and Its Properties
1.6: Exploring Transformations of Parent Functions
1.7: Investigating Horizontal Stretches, Compressions, and Reflections
1.8: Using Transformations to Graph Functions of the Form y = af [k(x - d )] + c

### CHAPTER 2: Equivalent Algebraic Expressions

2.2: Multiplying Polynomials
Curious Math
2.3: Factoring Polynomials
2.4: Simplifying Rational Functions
2.5: Exploring Graphs of Rational Functions
2.6: Multiplying and Dividing Rational Expressions

3.2: Determining Maximum and Minimum Values of a Quadratic Function
3.3: The Inverse of a Quadratic Function
3.6: The Zeros of a Quadratic Function

### CHAPTER 4: Exponential Functions

4.1: Exploring Growth and Decay
4.2: Working with Integer Exponents
4.3: Working with Rational Exponents
4.4: Simplifying Algebraic Expressions Involving Exponents
4.5: Exploring the Properties of Exponential Functions
4.6: Transformations of Exponential Functions
4.7: Applications Involving Exponential Functions

### CHAPTER 5: Trigonometric Ratios

5.1: Trigonometric Ratios of Acute Angles
5.2: Evaluating Trigonometric Ratios for Special Angles
Curious Math
5.3: Exploring Trigonometric Ratios for Angles Greater than 90°
5.4: Evaluating Trigonometric Ratios for Any Angle Between 0° and 360°
5.5: Trigonometric Identities
5.6: The Sine Law
5.7: The Cosine Law
5.8: Solving Three-Dimensional Problems by Using Trigonometry

### CHAPTER 6: Sinusoidal Functions

6.1: Periodic Functions and Their Properties
6.2: Investigating the Properties of Sinusoidal Functions
6.3: Interpreting Sinusoidal Functions
6.4: Exploring Transformations of Sinusoidal Functions
6.5: Using Transformations to Sketch the Graphs of Sinusoidal Functions
6.6: Investigating Models of Sinusoidal Functions
6.7: Solving Problems Using Sinusoidal Models

### CHAPTER 7: Discrete Functions: Sequences and Series

7.1: Arithmetic Sequences
7.2: Geometric Sequences
7.3: Creating Rules to Define Sequences
7.4: Exploring Recursive Sequences
Curious Math
7.5: Arithmetic Series
7.6: Geometric Series
7.7: Pascal's Triangle and Binomial Expansions

### CHAPTER 8: Discrete Functions: Financial Applications

8.1: Simple Interest
8.2: Compound Interest: Future Value
8.3: Compound Interest: Present Value
Curious Math
8.4: Annuities: Future Value
8.5: Annuities: Present Value
8.6: Using Technology to Investigate Financial Problems

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### Chapter 1: Algebraic Tools for Operating With Functions

1.1: Reviewing the Exponent Laws
1.2: Rational Exponents
1.3: Solving Exponential Equations
1.4: Review: Adding, Subtracting, and Multiplying Polynomials
1.5: Simplifying Rational Expressions
1.6: Multiplying and Dividing Rational Expressions
1.7: Adding and Subtracting Rational Expressions, I
1.8: Adding and Subtracting Rational Expressions, II
1.9: Solving First-Degree Inequalities

### CHAPTER 2: Quadratic Functions and Equations

2.1: The Complex Number Syste
2.2: Maximum or Minimum of a Quadratic Function by Completing the Squar
2.4: Tools for Operating With Complex Numbers
2.5: Operations With Complex Numbers in Rectangular Form

### CHAPTER 3: Transformations of Functions

3.1: Functions
3.2: Investigation:Properties of Functions Defined by f(x) = √ − x and f(x) = 1 – x
3.3: Horizontal and Vertical Translations of Functions
3.4: Reflections of Functions
3.5: Inverse Functions
3.6: Stretches of Functions
3.7: Combinations of Transformations

### CHAPTER 4: Trigonometry

4.1: Reviewing the Trigonometry of Right Triangles
4.2: The Sine and the Cosine of Angles Greater Than 90°
4.3: The Sine Law and the Cosine Law
4.4: The Sine Law: The Ambiguous Case

### CHAPTER 5: Trigonometric Functions

5.2: Trigonometric Ratios of Any Angle
5.3: Modelling Periodic Behaviour
5.4: Investigation: Sketching the Graphs of f(x) = sin x, f(x) = cos x, and f(x) = tan x
5.5: Stretches of Periodic Functions
5.6: Translations and Combinations of Transformations
5.7: Trigonometric Identities
5.8: Trigonometric Equations

### CHAPTER 6: Sequences and Series

6.1: Sequences
6.2: Arithmetic Sequences
6.3: Geometric Sequences
6.4: Recursion Formulas
6.5: Arithmetic Series
6.6: Geometric Series

### CHAPTER 7: Compound Interest and Annuities

7.1: Investigation: Simple Interest, Arithmetic Sequences, and Linear Growth
7.2: Compound Interest
7.3: Investigation: Compound Interest, Geometric Sequences, and Exponential Growth
7.4: Present Value
7.5: Amount of an Ordinary Annuity
7.6: Present Value of an Ordinary Annuity
7.7: Technology: Amortization Tables and Spreadsheets
7.8: Mortgages

### CHAPTER 8: Loci and Conics

8.1: Technology: Constructing Loci Using The Geometer’s Sketchpad®
8.2: Equations of Loci
8.3: Technology: Loci and Conics
8.4: The Circle
8.5: The Ellipse
8.6: The Hyperbola
8.7: The Parabola
8.8: Conic Sections With Equations in the Form ax2 + by2 + 2gx + 2fy + c = 0
8.9: Intersections of Lines and Conics # Strictly Ontario Curriculum

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