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Grade 11 Functions (MCR3U)

University Preparation 
Prerequisite: Principles of Mathematics, Grade 10, Academic

Learning Objectives:
Grade 11 Functions:

          - Representing Functions
          - Solving Problems Involving Quadratic Functions
          - Determining Equivalent Algebraic Expressions

          - Representing Exponential Functions
          - Connecting Graphs and Equations of Exponential Functions
          - Solving Problems Involving Exponential Functions

          - Representing Sequences
          - Investigating Arithmetic and Geometric Sequences and Series
          - Solving Problems Involving Financial Applications

          - Determining and Applying Trigonometric Ratios
          - Connecting Graphs and Equations of Sinusoidal Functions
          - Solving Problems Involving Sinusoidal Functions



Functions 11 - Nelson










Table of Contents

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