Function Transformations: Translation

The red curve above is a “transformation” of the green one. It has been “translated” (or shifted) four units to the right. A translation is a change in position resulting from addition or subtraction, one that does not rotate or change the size or shape in any way.

Transformations are often easiest to analyze by focusing on how the location of specific  points on the curve have changed. In the image above, the point A_1 on the green curve “corresponds” to point A_2 on the red curve. By this we mean that the transformation has moved point A_1 to A_2.

Horizontal Translations

In looking at the coordinates of the two corresponding points identified in the graph above, you can see that the y-coordinate has not changed and the x-coordinate has increased by 4. If you were to examine any other pair of corresponding points, you would see the exact same difference. This can be described algebraically by the equation:

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