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Functions

Grade 11 University Mathematics, following the Ontario curriculum.

  • 4 units
  • 38 lessons
  • 431 practice questions
  • 340 flashcards
  • 4 simulators
Start Unit 1Exam review →
Try oneMCR3U · Relations vs. Functions
Which set of ordered pairs is NOT a function?

Units

Unit 1 · 12 lessons · ~40% of course

Characteristics of Functions

How to recognize, evaluate, transform and invert functions, and the algebra (quadratics, radicals, rational expressions) that supports working with them.

  1. 1Relations vs. Functions
  2. 2Domain and Range
  3. 3Parent Functions
  4. 4Transformations of Functions
  5. 5Inverse Functions
  6. 6Forms of a Quadratic Relation
  7. 7Completing the Square
  8. 8Solving Quadratic Equations
  9. 9Quadratic Applications
  10. 10Radicals
  11. 11Rational Expressions
  12. 12Equivalent Algebraic Expressions
Unit 2 · 8 lessons · ~15% of course

Exponential Functions

Exponent rules, the shape and transformations of y = bˣ, and real growth/decay models — populations, half-life, depreciation.

  1. 1Exponent Laws
  2. 2Rational Exponents and Radicals
  3. 3Graphs of Exponential Functions
  4. 4Linear, Quadratic or Exponential?
  5. 5Transformations of Exponential Functions
  6. 6Finding an Exponential Equation
  7. 7Solving Exponential Equations
  8. 8Exponential Growth and Decay Applications
Unit 3 · 8 lessons · ~10% of course

Discrete Functions

Sequences, series, Pascal's triangle, and the financial math (interest and annuities) that sequences make possible.

  1. 1Sequences as Discrete Functions
  2. 2Arithmetic Sequences
  3. 3Geometric Sequences
  4. 4Arithmetic Series
  5. 5Geometric Series
  6. 6Pascal's Triangle and the Binomial Theorem
  7. 7Simple and Compound Interest
  8. 8Simple Annuities
Unit 4 · 10 lessons · ~35% of course

Trigonometric Functions

From right-triangle trig through the sine and cosine laws to sinusoidal graphs and real-world modelling — all in degrees.

  1. 1Right Triangle Trigonometry
  2. 2Special Triangles and Exact Values
  3. 3Angles from 0° to 360° and the CAST Rule
  4. 4The Sine Law
  5. 5The Ambiguous Case of the Sine Law (SSA)
  6. 6The Cosine Law
  7. 7Trigonometric Identities
  8. 8Periodic Functions: Period, Amplitude, and Axis
  9. 9Graphs of y = sin x and y = cos x — Transformations
  10. 10Modelling with Sinusoidal Functions

Simulators

Simulators for every course →
MCR3U
Function Transformer

Drag a, k, d and c and watch any parent function stretch, flip and slide.

Used in 5 lessons
MCR3U
Unit Circle Explorer

Drag the terminal arm to see exact ratios, reference angles and CAST signs.

Used in 5 lessons
MCR3U
Sinusoid Builder

Build a sine or cosine curve, then play match-the-graph against a random target.

Used in 3 lessons
MCR3U
Sequences & Finance

Terms, series sums, compound interest and annuities with the formulas filled in.

Used in 2 lessons