Combinations of Transformations (CIE A Level Maths: Pure 1)

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Combinations of Transformations

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

 

Combinations What Is, A Level & AS Level Pure Maths Revision Notes

 

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 the horizontal transformation inside the brackets if there is one
      • y kf(ax)+ or y kf(x + 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)+ or y kf(x + 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)

Examiner Tip

  • Be sure to apply transformations in the correct order – applying them in the wrong order can produce an incorrect transformation. 
  • When you sketch a transformed graph, indicate the new coordinates of any points that are marked on the original graph.
  • Try to indicate the coordinates of points where the transformed graph intersects the coordinate axes (although if you don't have the equation of the original function this may not be possible).
  • If the graph has asymptotes, don't forget to sketch the asymptotes of the transformed graph as well.

Worked example

 Comb Xforms Example, A Level & AS Level Pure Maths Revision Notes

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Roger

Author: Roger

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.