Transformations of Functions
A transformation of a function is a way of mapping that function to another.
The most commonly asked question in an exam on this topic is: Which geometrical transformation maps the graph y = f(x) to y = g(x)?
There are three types of transformation: translations, stretches and reflections. This revision sheet will take you through all three in a step-by-step manner, including some exam tips for how to obtain full marks on any transformation question.
An important element to remember when doing any form of transformation is
A translation is a type of transformation which moves a function from one position to another. These are always written in vector form and are recognised through the process of addition/subtraction.
y = x^2 maps to y = (x^2) + 2
Here, the geometrical transformation would be described as a:
2 where the 0 and 2 are enclosed in a single bracket.
This is because, according to VON HIR, the action we are doing to the function of x (x^2 in this case) is outside of the function we began with, meaning it is a vertical translation (in the y-direction) and is taken as it is.
If we mapped y = x^2 to y = (x+2)^2
the transformation would then become:
VON HIR dictates that anything INSIDE the function we began with is in the x-direction (horizontal) and becomes reversed (i.e. positive becomes negative)
y = x^2 maps to y = ((x+2)^2) + 2 would be described as a:
To generalise: if y = f(x) maps to y = f(x-a) + b
the geometrical transformation used to describe it would be a