Mathematics: Applications and Interpretation · Topic 2: Functions

AHL2.8 — Transformations of graphs

Mathematics: Applications and Interpretation · SL / HL · syllabus-mapped notes

1. AIAHL2.8.1

   Translations and reflections

   $y=f(x)+b$ and $y=f(x-a)$ shift the graph; $y=-f(x)$ and $y=f(-x)$ reflect it in the axes.

2. AIAHL2.8.2

   Stretches

   $y=p\,f(x)$ is a vertical stretch (factor $p$); $y=f(qx)$ is a horizontal stretch (factor $\tfrac{1}{q}$).

3. AIAHL2.8.3

   Composite transformations

   Combining transformations, where the order applied changes the result.