Functions (MCR3U)

By the end of this course, students will:

• demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations;
• determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications;
•  demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.

By the end of this course, students will:

• evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways;
•  make connections between the numeric, graphical, and algebraic representations of exponential functions;
• identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications.

By the end of this course, students will:

• demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle;
•  demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems;
• make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities.

By the end of this course, students will:

• determine the values of the trigonometric ratios for angles less than 360º; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law;
• demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions;
• identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications