Advanced Functions

MHF4U deepens students’ understanding of mathematical functions and their applications.

The course focuses on

• Algebraic skills
• Polynomial
• Rational
• Expressions
• Advanced function types including exponential
• Logarithmic
• Trigonometric functions.

Emphasis is placed on solving equations, analyzing function behaviour, and modeling real-world situations, preparing students for university-level mathematics, science, and business programs.

Unit 1: Function Properties and Transformations
Students explore the characteristics and manipulation of functions.
Lessons include:

• Introduction to Functions
• Adding, Subtracting, and Multiplying Functions
• Inverse Functions
• Transformations of Graphs
• Composition of Functions
• Average and Instantaneous Rate of Change

Unit 2: Polynomial and Rational Functions
This unit examines algebraic expressions and equations.
Lessons include:

• Polynomial Functions and Their Features
• Graphing Polynomial Functions
• Factoring Techniques
• Remainder and Factor Theorems
• Rational Functions and Graphs
• Solving Polynomial and Rational Equations
• Inequalities with Polynomials and Rationals

Unit 3: Trigonometric Functions
Students build on prior trigonometry knowledge and expand into advanced applications.
Lessons include:

• Introduction to Logarithms
• Laws of Logarithms and Exponent Rules
• Exponential and Logarithmic Equations
• Graphing and Transforming Exponential/Log Functions
• Real-Life Applications in Finance, Biology, and Physics

Unit 4: Final Evaluation
Students apply their knowledge in problem-solving and analysis tasks.
Lessons include:

• Culminating Mathematical Modeling Project
• Final Exam

• 70% of the final grade is based on coursework, including:
  • Function graphing and transformation tasks
  • Algebraic manipulation and identity proofs
  • Application problems involving finance, growth, and motion
  • Unit quizzes, assignments, and reflections
• 30% of the final grade is based on final evaluations:
  • 10% Culminating application project
  • 20% Final written exam assessing all function types and problem-solving skills

All assessments follow Ontario curriculum standards and are designed to support mathematical fluency, critical thinking, and analytical modeling essential for postsecondary success