P3.1.4 - Combined transformations of functions

Combine transformations y = af(x), y = f(x) + a, y = f(x + a) and y = f(ax), and sketch the resulting graphs; transformations of the form y = f(ax + b) are not required.

Use combined transformations of functions to connect the rule to the data and decision in the question.

This matters because combined transformations of functions determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply combined transformations of functions to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Combined transformations of functions is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.