Combinations of Transformations (AQA A Level Maths: Pure)

What are combinations of graph transformations?

• When you alter a function in certain ways, the effects on the graph of the function can be described by geometrical transformations
• In additional to single transformations, you need to be able to interpret the effects of multiple transformations applied to the same function

How do I combine two or more graph transformations?

• Make sure you understand the effects of individual translations, stretches, and reflections on the graph of a function (see the previous pages)
• When applying combinations of these transformations, apply them to the graph one at a time according to the following guidelines:
  • First apply any horizontal transformations inside the brackets (if you have more than one transformation inside the brackets, translations must be applied before stretches and reflections)
    • y = kf(ax + b)+ c
  • Then apply any vertical transformations outside the brackets (if you have more than one transformation outside the brackets, stretches and reflections must be applied before translations)
    • y = kf(ax + b)+ c

• Any asymptotes of the function are also affected by the combined transformation (perform the transformations one at a time in the same order as above)