# MCR3U

Functions - 11

#### Course Description:

This course introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

Prerequisite: MPM2D - Principles of Mathematics Grade 10

##### Course Outline

Unit 1: Characteristics of Functions (30 hours)

The idea of a function is very important in mathematics because it describes any situation in which one quantity depends on another. For example, the height of a person depends on his age. The distance an object travels in four hours depends on its speed. In previous mathematics courses, you have studied linear relations and some non-linear relations. In this unit, you will learn what distinguishes some relations as functions. You will represent them in a variety of ways. Your understanding of the quadratic function will be extended and you will apply your knowledge of quadratics to real-life situations.

LESSON # LESSON NAME
1-1 Presenting Functions
1-2 Transformations of Functions
1-3 Combinations of Transformations
1-4 Inverse Functions
1-5 Maximum of Minimum and the Zeroes of a Quadratic Function
1-6 Equivalent Algebraic Expressions
1-8 Intersection of a Linear Function and a Quadratic Function

Unit 2: Discrete Functions (25 hours)

In this unit, we will explore a wide variety of number patterns called sequences. We will learn that the sequences have many applications in fields such as medicine, biology, finances, and construction. We will also learn about financial concepts such as simple and compound interest, present value, and annuities that will help us solve real-world applications like a car payment, mortgage or retirement funds.

LESSON # LESSON NAME
2-1 Introduction to Sequences and Recursive Formulas
2-2 Arithmetic and Geometric Sequences
2-3 Arithmetic and Geometric Series
2-4 Pascal's Triangle
2-5 Simple and Compound Interests
2-6 Present Value
2-7 Ordinary Simple Annuities

Unit 3: Exponential Functions (20 hours)

When we think of exponents, we probably think of repeated multiplication. In this unit, we will extend our knowledge of exponents and exponential functions. What does a zero exponent mean? What about negative and fractional exponents? What do such numbers have to do with the growth of living organisms, nuclear power generation, and investments and loans? Questions like these will be answered in this unit.

LESSON # LESSON NAME
3-1  Exponential Relations
3-2 Properties of Exponential Functions
3-3 Transformations
3-4 Exponential Equations

Unit 4: Trigonometric Functions (35 hours)

In this unit, we will learn how trigonometry can be used to overcome these types of challenges. We will also investigate the basic trigonometric functions and learn how to transform them. Lastly using those transformations, we will develop models for real-world applications.

LESSON # LESSON NAME
4-1 Trigonometric Ratios and Special Angles
4-2 Sine and Cosine Laws
4-3 Trigonometric Identities
4-4 Modelling Periodic Behaviour
4-5 Graphs of Sine and Cosine Functions
4-6 Transformations of Sinusoidal Functions
4-7 Applications of Sinusoidal Functions