The type of transformation that preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x) is vertical translation.
Vertical translation of a graph is done by moving the base graph up or down in the y-axis direction. Each point on a graph is moved k units vertically to translate the graph by that many units.
The vertical translation is the movement of the curve along the y-axis by a certain number of units without altering the function's shape or domain.
The function's form is preserved in the case of vertical translation.
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