Combined Transformations of Functions in MYP Extended Maths
Master combined function transformations in MYP Extended Maths Year 5. Learn the correct order of applying translations, reflections and stretches with exam strategies.
Putting It All Together
Combined transformations apply two or more of the individual transformation types — translations, reflections, and stretches — to a single function. This is the most demanding transformation topic at Extended level because the order in which transformations are applied matters and can produce different results if done incorrectly.
Order of Transformations
When reading a transformed function such as y = af(bx + c) + d, the standard approach is to apply transformations in the following order:
- Horizontal translation by −c/b (handle the inside of the function first).
- Horizontal stretch by scale factor 1/b.
- Vertical stretch by scale factor a.
- Vertical translation by d.
In practice, many problems can be reasoned through by tracking the effect on a small set of key points rather than memorising a fixed rule. Trace what happens to two or three labelled points through each step.
Reading Combined Transformations from an Equation
Given y = 2f(x − 3) + 1: identify the vertical stretch (factor 2), the horizontal translation (right 3), and the vertical translation (up 1). Sketch the base function f(x) first, then apply each transformation in sequence, redrawing after each step.
Writing the Equation from a Description or Graph
A Criterion C task may show you two graphs and ask you to describe the sequence of transformations, or give you a description and ask you to write the equation. Practise both directions: equation to description, and description to equation.
Common Mistakes
- Applying transformations in the wrong order, especially when both a horizontal stretch and translation are involved.
- Describing a combined transformation with a single vague statement rather than listing each step precisely.
- Confusing the sign of a horizontal translation inside the function bracket.
Exam Strategy
For multi-mark transformation questions, show each step of your reasoning. A clear, sequential approach earns method marks even if the final graph has a minor error. Criterion C rewards precise mathematical language — use terms like translate, reflect, and stretch with their correct parameters.