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

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