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# C2/ C3 Composite transformations Watch

1. Hey, I am just writing up some rev notes and I don't really have aprticularly great notes on composite transformations so I was wondering if anyone can write the rules for me, like what are the orders for x and y transformations like translations, SF stretches and reflections.

Help much appreciated! (+ rep for most helpful )
2. (Original post by daftndirekt)
Hey, I am just writing up some rev notes and I don't really have aprticularly great notes on composite transformations so I was wondering if anyone can write the rules for me, like what are the orders for x and y transformations like translations, SF stretches and reflections.

Help much appreciated! (+ rep for most helpful )
Generally follow this for applying tranformations:

x-translation

x-stretch

y-stretch

y-translation

Reflections come under stretches.
3. (Original post by daftndirekt)
Hey, I am just writing up some rev notes and I don't really have aprticularly great notes on composite transformations so I was wondering if anyone can write the rules for me, like what are the orders for x and y transformations like translations, SF stretches and reflections.
If you have a linear equation then expand out the brackets.

e.g. Expand 2(3x+1)+4, but not 2(3x+1)^3+4. You will find expanding out polynomial functions of degree 2 or greater to be of no use.

NB: It would be wise to look up the definition of a polynomial if you don't know it.

Next get a base graph. In the case of 2(3x+1)^3+4 your base graph would be x^3.

Start by applying the inner most transformation, working your way out.

First apply the x-stretch, scale factor 1/3 to get (3x)^3

Next apply the translation, one unit left to get (3x+1)^3

Now apply the y-transformations.

So apply the y-stretch, scale factor 2 to get 2(3x+1)^3

Next apply the translation 4 units up to get 2(3x+1)^3+4

The reason it is done in this order is to prevent transformations interfering with each other. If you do them in any other way you will notice that transformations can mess each other up so some care should be taken.

It is wise to draw a quick sketch at each stage to get a rough idea of how the function should look. The sketch should contain all intecepts and turning points (although the TPs need not be defined).

To remember quickly what to do - here's a quick reminder:

x takes precedence over y
stretches take precedence over translations

I think that should be everything.

Darren

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