A vertical translation refers to the shifting of a function either up or down on the coordinate axis. This is done by adding or subtracting a constant value to the function.
Example: y = x² + 3 represents a vertical translation of the graph of y = x² three units upward.
A horizontal translation refers to the shifting of a function either to the left or to the right on the coordinate axis. This is done by adding or subtracting a constant value to the independent variable in the function.
Example: y = (x-2)² represents a horizontal translation of the graph of y = x² two units to the right.
To determine the direction and amount of the translation, look at the added or subtracted value in the function. If it is added, the translation is in the opposite direction (up or left), and if it is subtracted, the translation is in the same direction (down or right).
Vertical & Horizontal Translations Quick Check
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