Advanced Mathematical Thinking™
Grades 9 & 10
Functions
Function families, transformations, composition, inverses, and modeling with functions.
1
Function Families
Linear, quadratic, exponential, and piecewise functions as objects.
2
Transformations
Shifting, reflecting, and scaling functions.
3
Composition & Inverses
Combining and reversing functions.
Definition
Functions in one line
Function families, transformations, composition, inverses, and modeling with functions.
Every course builds on the last; each opens the next.
Where this leads next
Functions→Mathematical Modeling
Mastering Functions unlocks the reasoning structures of Mathematical Modeling.
Sample challenges
AdvancedApproachable
Foundational Problem
A representative problem for this course — accessible now, with room to generalize.
Functions
AdvancedChallenging
Stretch Problem
A problem that extends the course's core ideas into non-routine territory.
FunctionsReasoning
AdvancedOlympiad
Transfer Problem
Apply this course's structure to a competition or advanced context.
FunctionsTransfer