This course extends the students’ experience with functions. Students will investigate and apply the properties of polynomial, rational, logarithmic and trigonometric functions; broaden their understanding of rates of change; and develop facility with the application of these concepts and skills.Students will continue to develop the mathematical processes necessary for success in senior mathematics.
Strands:
Polynomial and Rational Functions
Exponential and Logarithmic Functions
Trigonometric Functions
Characteristics of Functions / Pre-requisite:Functions (MCR3U)
Mathematical Processes:
Problem Solving
Reasoning and Proving
Reflecting
Selecting Tools and Computational Strategies
Connecting
Representing
Communicating
Course Overview:
Polynomial and Rational Functions
Identify and describe some key features of a polynomial or rational functions and use these features to sketch or graph the functions;
Determine the real roots of factorable and non-factorable polynomials using a variety of tools and strategies;
Solve factorable and non-factorable polynomial and rational inequalities using a variety of tools and strategies;
Exponential and Logarithmic Functions:
Demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms and simplify logarithmic expressions using the laws of logarithms;
Make connections between the numeric, graphical and algebraic representations of logarithmic functions;
Solve exponential and logarithmic equations and solve related problems, including those arising from real world applications;
Trigonometric Functions:
Demonstrate an understanding of the meaning and application of radian measure;
Make connections between the algebraic and graphical representations of trigonometric functions, their reciprocals and their inverses; and use these connections to solve problems;
Solve problems involving trigonometric equations and prove trigonometric identities using a variety of tools and strategies;
Characteristics of Functions:
determine and interpret the average rate of change for a function over a given interval and the instantaneous rate of change for a function at a given point;
describe some properties of compound functions and determine the composition of two functions using a variety of tools and strategies,
DRAFT OF ADVANCED FUNCTIONS - NOT FOR PUBLICATION
Last printed 14/09/2006 2:39 PM