Vertical translation

In geometry, a vertical translation is a translation of a geometric object in a direction parallel to the vertical axis of the Cartesian coordinate system.

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The graphs of different antiderivatives of the function f(x) = 3x² − 2. All are vertical translates of each other.

Often, vertical translations are considered for the graph of a function. If f is any function of x, then the graph of the function f(x) + c (whose values are given by adding a constant c to the values of f) may be obtained by a vertical translation of the graph of f(x) by distance c. For this reason the function f(x) + c is sometimes called a vertical translate of f(x). For instance, the antiderivatives of a function all differ from each other by a constant of integration and are therefore vertical translates of each other.