MHF4U University Preparation
Advanced Functions

Course Summary

Subject Area Subject: Mathematics

Grade 12


1 Credit

4 Units, 41 learning activities

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. 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.

Course outline

Learning Activity 1 Recognizing applications of polynomial expressions

Learning Activity 2 Describing polynomial expressions


Learning Activity 3 Identifying polynomial functions

Learning Activity 4 Classifying polynomial functions

Learning Activity 5 Exploring the effect of degree on polynomial functions

Learning Activity 6 Determining the end behaviours of polynomial functions

Learning Activity 7 Describing polynomials in factored form

Learning Activity 8 Developing the factor theorem and remainder theorem

Learning Activity 9 Applying long division to polynomial functions

Learning Activity 10 Investigating transformations of polynomial functions

Learning Activity 11 Using symmetry to characterize odd and even polynomial functions

Learning Activity 12 Exploring the graphs of reciprocal functions

Learning Activity 13 Connecting algebraic and graphical representations of rational functions

Learning Activity 14 Solving rational equations

Learning Activity 15 Solving inequalities