If function transformation was talked about in terms of geometric transformations it may be clearer why functions translate horizontally the way they do. A graph is translated k units horizontally by moving each point on the graph k units horizontally.įor the base function f( x) and a constant k, the function given by g( x) = f( x − k), can be sketched f( x) shifted k units horizontally. In function graphing, a horizontal translation is a transformation which results in a graph that is equivalent to shifting the base graph left or right in the direction of the x-axis. 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. For this reason the function f( x) + c is sometimes called a vertical translate of f( x). 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. Often, vertical translations are considered for the graph of a function. All graphs are vertical translations of each other. ![]() ![]() The graphs of different antiderivatives, F n( x) = x 3 − 2x + c, of the function f( x) = 3 x 2 − 2. In geometry, a vertical translation (also known as vertical shift) is a translation of a geometric object in a direction parallel to the vertical axis of the Cartesian coordinate system. For the concept in physics, see Vertical separation.
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