What are Transformations of Graphs?
A transformation is simply a change of some sort. When it comes to graphs you need to know about two different sorts of transformation:
- Reflections (using either the x-axis or y-axis as a mirror line)
- Translations (moving the whole curve in the x and/or y direction)
You should be able to recognise these two different sorts of transformation and apply them to a given graph.
How do we recognise and apply them?
If you are given the graph of a function, say y = f(x) then:
- REFLECTIONS look like this:
- In x-axis: y = -f(x) (minus outside the function)
- In y-axis: y = f(-x) (minus inside the function)
- + a units in the x direction: y = f(x – a)
- + b units in the y direction: y = f(x) + b
- BEWARE the highlighted change of sign!