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…
fx
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.
