_{^{Up Learn – A Level maths (edexcel) – Transforming Curves}}

Transformations: Summary

Here’s a summary of everything you need to know about transformations.

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1. Introduction to Transforming Curves (free trial)
2. Six Ways to Transform a Curve (free trial)
3. f(x) + a: Translation Up and Down Part 1 (free trial)
4. f(x) + a: Translation Up and Down Part 2 (free trial)
5. -f(x): Reflection in the Horizontal Axis Part 1 (free trial)
6. -f(x): Reflection in the Horizontal Axis Part 2 (free trial)
7. What Do We Mean by ‘Stretching and Squashing’? (free trial)
8. af(x): Vertical Stretching and Squashing (free trial)
9. f(x + a): Translation Left and Right Part 1 (free trial)
10. f(x + a): Translation Left and Right Part 2 (free trial)
11. f(-x): Reflection in the Vertical Axis Part 1 (free trial)
12. f(-x): Reflection in the Vertical Axis Part 2 (free trial)
13. f(ax): Horizontal Stretching and Squashing Part 1 (free trial)
14. f(ax): Horizontal Stretching and Squashing Part 2 (free trial)
15. f(ax): Horizontal Stretching and Squashing Part 3 (free trial)

There are six ways to transform a curve:

Translating it up or down, and translating it left to right.

Reflecting it in the horizontal axis, and reflecting it in the vertical axis.

Stretching or squashing the curve vertically , and stretching or squashing the curve horizontally.

For any given function…

This represents a translation up… or down.

This represents a translation left… or right.

This represents a reflection in the horizontal axis… and this, a reflection in the vertical axis.

This represents a squash towards the horizontal axis… and this a stretch away from the horizontal axis.

Finally this represents a stretch away from the vertical axis… and this a squash towards it.

To sketch one of these three types of transformation, pick a few points on the curve… transform the y-coordinates of their points… and then sketch in the transformed curve.

To sketch one of these three types of transformation, pick a few points on the curve… and this time work out what new x-coordinate you need to map to the existing x-coordinate. Then plot the new x-coordinates against the outputs and sketch in the transformed curve.

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Up Learn – A Level maths (edexcel) – Transforming Curves