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# Grade 11 Functions (MCR3U)

University Preparation

Prerequisite: Principles of Mathematics, Grade 10, Academic

# Learning Objectives:

Grade 11 Functions:

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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

## Functions 11 - Nelson

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## Table of Contents

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### 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

2.1: Adding and Subtracting Polynomials

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

### CHAPTER 3: Quadratic Functions

3.1: Properties of Quadratic Functions

3.2: Determining Maximum and Minimum Values of a Quadratic Function

3.3: The Inverse of a Quadratic Function

3.4: Operations with Radicals

Curious Math 3.5: Quadratic Function Models: Solving Quadratic Equations

3.6: The Zeros of a Quadratic Function

3.7: Families of Quadratic Functions

3.8: Linear–Quadratic Systems

### 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