01
Polynomial functions
Algebraic structure predicts zeros, multiplicity, symmetry, and end behaviour.
Learning goals
- Apply the factor and remainder theorems
- Solve polynomial equations
- Sketch from features
Core formulas
Factored polynomial
MHF4U · Advanced Functions
Grade 12 Advanced Functions
Analyze polynomial, rational, exponential, logarithmic, and trigonometric functions while preparing for calculus and university mathematics.
02
Rational functions
Restrictions, factors, and degrees reveal holes, vertical asymptotes, and end behaviour.
Learning goals
- State restrictions
- Distinguish holes from asymptotes
- Solve rational equations
Core formulas
Rational function
03
Exponential and logarithmic functions
Logarithms reverse exponentiation and turn multiplicative relationships into additive ones.
Learning goals
- Apply exponent and log laws
- Solve exponential equations
- Model growth and decay
Core formulas
Exponential model
Log definition
04
Trigonometric functions and identities
Equivalent identities reveal the same trigonometric relationship in different forms.
Learning goals
- Prove identities
- Solve equations
- Model periodic phenomena
Core formulas
Pythagorean identity