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1. Successive Transformations

Combining transformations

There have already been rules (from Core 1) for the transformation of a given function from another, subject to the differences between the two functions. It is often the case that when transformations are carried out in succession there will need to be consideration of the order of the transformations.

Consider that if the graph is transformed onto the graph of , it is not possible to conduct a translation in the negative y-direction of 2, and then stretch parallel to the y-axis by a scale factor of 2, as this would yield (note that this could be sorted out through the employment of another translation in the y-direction, however this is undesirable). One way that this transformation could be done is by doing the stretch first, and then the translation.

As it is possible to tell, the original idea is almost correct, a stretch could be employed after a translation, however the translation would have to be a unit in the negative y-direction (as opposed to 2 units), as .

Example

1. Describe two ways in which the graph of could be translated onto the graph of ("n" is a constant).

Simply use the same idea as discussed previously:

Stretch parallel to the y-axis, scale factor "n", and then translate "n" units in the negative y-direction.

A second method can also be approached through a factorisation technique:

Hence a translation of a single unit in the negative y-direction could be followed by a stretch parallel to the y-axis, scale factor "n".

Also See

Read these other OCR Core 3 notes:

1. Successive transformations
2. Functions
3. Exponential growth and decay
4. Extending differentiation and integration

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