IB Maths AI SL 2.2 - Functions Notes

This IB Maths AI SL 2.2 resource introduces functions, domain and range, and inverse functions, and is fully aligned with the IB Applications and Interpretation SL syllabus.

Students learn what it means for a relation to be a function, including the key idea that each input must map to exactly one output. The notes introduce function notation and help students understand how a rule connects elements from a domain to elements in a range.

The resource develops the concepts of domain, range, and graph through clear definitions and examples. Students practise interpreting possible inputs and outputs, including square-root functions where the expression inside the root must be non-negative and the resulting outputs are restricted.

Inverse functions are then introduced informally as functions that reverse the effect of the original function. Students learn that an inverse swaps the roles of the domain and range, uses the notation (f^{-1}(x)), and can be understood graphically as a reflection in the line (y=x).

The notes also explain why domain restrictions may be needed, using (f(x)=x^2) as an example of a function that is not one-to-one unless its domain is restricted. This prepares students to think carefully about when inverse functions exist and how their domains and ranges are connected.

Structured practice problems guide students through finding the domain and range of square-root and rational functions, before working through the inverse of a square-root function step by step. A graphical check reinforces the idea that a function and its inverse are mirror images in the line (y=x).

Ideal for IB Maths AI SL teachers teaching functions, domain and range, function notation, inverse functions, domain restrictions, and graphical interpretations of inverses.

This pairs great with our slidedeck!