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###### This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. 该课程扩展了学生在功能方面的经验。 学生将研究多项式，有理，对数和三角函数的性质； 开发组合功能的技术； 加深他们对变化率的理解； 并发展应用这些概念和技能的设施。

MHF4U – Advanced Functions course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs.

### 课程体系

 CHAPTER 1 - POLYNOMIAL FUNCTIONS 1.0 Prerequisite Skills 00:00:00 1.1 Power Functions 00:00:00 1.2 Characteristics of Polynomial Functions 00:00:00 1.3 Equations and Graphs of Polynomial Functions 00:00:00 1.4 Transformation 00:00:00 1.5 Slopes of SECANTS and Average Rate of Change 00:00:00 1.6 Slopes of TANGENTS and Instantaneous Rate of Change 00:00:00 CHAPTER 2 - POLYNOMIAL EQUATIONS & INEQUALITIES 2.1 The Remainder Theorem – Part 1 00:00:00 2.1 The Remainder Theorem – Part 2 00:00:00 2.1 The Remainder Theorem – Part 3 00:00:00 2.2 The Factor Theorem 00:00:00 2.3 Polynomial Equations – Part 1 00:00:00 2.3 Polynomial Equations – Part 2 00:00:00 2.3 Polynomial Equations – Part 3 00:00:00 2.4 Families of Polynomial Functions – Part 1 00:00:00 2.4 Families of Polynomial Functions – Part 2 00:00:00 2.5 Solve Inequalities Using Technology 00:00:00 2.6 Solve Factorable Polynomial Inequalities Algebraically – Part 1 00:00:00 2.6 Solve Factorable Polynomial Inequalities Algebraically – Part 2 00:00:00 CHAPTER 3 - RATIONAL FUNCTIONS 3.1 Reciprocal of a Linear Functions – Part 1 00:00:00 3.1 Reciprocal of a Linear Functions – Part 2 00:00:00 3.2 Reciprocal of a Quadratic Functions – Part 1 00:00:00 3.2 Reciprocal of a Quadratic Functions – Part 2 00:00:00 3.2 Reciprocal of a Quadratic Functions – Part 3 00:00:00 3.2 Reciprocal of a Quadratic Functions – Part 4 00:00:00 3.3 Rational Functions of the form f(x) = [ax + b] / [cx + d] 00:00:00 3.4 Solve Rational Equations and Inequalities – Part 1 00:00:00 3.4 Solve Rational Equations and Inequalities – Part 2 00:00:00 3.4 Solve Rational Equations and Inequalities – Part 3 00:00:00 3.5 Making Connections with Rational Functions and Equations 00:00:00 CHAPTER 4 - TRIGONOMETRY 4.1 Radian Measure 00:00:00 4.2 Trigonometric Ratios and Special Angles 00:00:00 4.3 Equivalent Trigonometric Expressions 00:00:00 4.4 Compound Angle Formulas – Part 1 00:00:00 4.4 Compound Angle Formulas – Part 2 00:00:00 4.5 Prove Trigonometric Identities (from MCR3U) 00:00:00 4.5 Prove Trigonometric Identities – Part 1 00:00:00 4.5 Prove Trigonometric Identities – Part 2 00:00:00 CHAPTER 5 - TRIGONOMETRIC FUNCTIONS 5.1 Graphs of Sine, Cosine and Tangent Functions 00:00:00 5.2 Graphs of Reciprocal Trigonometric Functions 00:00:00 5.3 Sinusoidal Functions of the Form:f(x) = a sin [k(x -d)] + c & f(x) = a cos [k(x -d)] + c – Part 1 00:00:00 5.3 Sinusoidal Functions of the Form:f(x) = a sin [k(x -d)] + c & f(x) = a cos [k(x -d)] + c – Part 2 00:00:00 5.3 Sinusoidal Functions of the Form:f(x) = a sin [k(x -d)] + c & f(x) = a cos [k(x -d)] + c – Part 3 00:00:00 5.3 Sinusoidal Functions of the Form:f(x) = a sin [k(x -d)] + c & f(x) = a cos [k(x -d)] + c – Graphing 00:00:00 5.4 Solve Trigonometric Equations – Part 1 00:00:00 5.4 Solve Trigonometric Equations – Part 2 00:00:00 5.5 Making Connections and Instantaneous Rate of Change (Sinusoidal Functions) 00:00:00 CHAPTER 6 - EXPONENTIAL & LOGARITHMIC FUNCTIONS 6.1 The Exponential Function and Its Inverse 00:00:00 6.2 Logarithms 00:00:00 6.3 Transformations of Logarithmic Functions 00:00:00 6.4 Power Law of Logarithms 00:00:00 6.5 Making Connection:Logarithmic Scales in the Physical Sciences 00:00:00 CHAPTER 7 - TOOLS & STRATEGIES FOR SOLVING EXPONENTIAL AND LOGARITHMIC EQUATIONS 7.1 Equivalent Forms of Exponential Equations 00:00:00 7.2 Techniques for Solving Exponential Equations – Part1 00:00:00 7.2 Techniques for Solving Exponential Equations – Part 2 00:00:00 7.3 Product and Quotient Law of Logarithmic – Part 1 00:00:00 7.3 Product and Quotient Law of Logarithmic – Part 2 00:00:00 7.4 Techniques for Solving Logarithmic Equations – Part 1 00:00:00 7.4 Techniques for Solving Logarithmic Equations – Part 2 00:00:00 7.5 Making Connection: Mathematical Modelling With Exponential and Logarithmic Equations 00:00:00 CHAPTER 8 - COMBINING FUNCTIONS 8.1 Sum and Differences of Functions – Part 1 00:00:00 8.1 Sum and Differences of Functions – Part 2 00:00:00 8.2 Products and Quotients of Functions 00:00:00 8.3 Composite Functions 00:00:00 8.4 Inequalities of Combined Functions 00:00:00 8.5 Making Connection: Modelling With Combined Functions 00:00:00

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