# Investigation of all four function transformations

- Author:
- joelsperanza

So far we have looked at all four function transformations in isolation. Now let's put it all together.
We've been using a for all our transformations so far, but we're going to introduce b, c, and d as well now.
The general form of these functions is:

**a(f(b(x+c)+d)**To break that down:**af(x) f(bx) f(x+c) f(x)+d**Set yourself a challenge to move a function in a particular way and try to achieve it.**For instance.**Left 5 spaces Up 3 spaces Stretched vertically by a factor of 2 Squashed horizontally by a factor of 3. Keep setting yourself new challenges and trying to achieve them until you are confident you can transform functions how you would like to do it.