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within 24 Hours ##### MCR3U

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.

## Course Outline

### Module 1 Overview: Characteristics of Functions

Guiding Question:
How do characteristics and transformations of a function determine its graph and its applications?

In this module, we will explore parent functions and their characteristics. These include linear, quadratic, square roots, and reciprocal functions. We will then focus on standard, factored and vertex form of quadratic equations to solve word problems.

### Module 2 Overview: Rational Functions

Guiding Question:
How can rational functions be simplified using different operations over their domain?

In this module, we will simplify, add, subtract, multiply and divide rational expressions, by using factoring and by considering the domain restrictions. We will begin to explore the graphs and applications of rational functions.

### Module 3 Overview: Exponents and Radicals

Guiding Question:
What strategies exist to simplify exponential and radical expressions?

In this module, we develop exponent laws to simplify expressions and to solve exponential equations. We explore the characteristics and transformations of exponential graphs, in order to apply exponential functions to growth and decay problems.

### Module 4 Overview: Trigonometric Functions and Equations

Guiding Question:
How can trigonometric functions and graphs be used to solve equations and model word problems?

In this module, we will investigate the properties of the graphs of the sine and cosine functions. We will explore transformations and applications of these functions. We will extend our knowledge of the sine and cosine laws to develop the ambiguous case of the sine law. We will apply special triangles and the CAST rule to solve trigonometric equations. We will learn techniques to prove trigonometric identities.

### Module 5 Overview: Discrete Functions

Guiding Question:
How can we express number patterns using general and recursive formulas?

In this module, we will develop general and recursive formulas for arithmetic and geometric sequences. We will compare the graphs of these discrete functions to linear and exponential functions, respectively. We will discover formulas for arithmetic and geometric series, to sum the terms of a sequence.

### Module 6 Overview: Financial Applications

Guiding Question:
How are exponential and linear functions related to compound and simple interest?

In this module, we will compare and contrast simple and compound interest calculations. We will rearrange these formulas to solve word problems. We will begin to explore ordinary simple annuities through timelines and formulas.