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.[1][2][3]

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).[4] 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.[5]

References

  1. De Berg, Mark; Cheong, Otfried; Van Kreveld, Marc; Overmars, Mark (2008), Computational Geometry Algorithms and Applications, Berlin: Springer, p. 91, doi:10.1007/978-3-540-77974-2, ISBN 978-3-540-77973-5.
  2. Smith, James T. (2011), Methods of Geometry, John Wiley & Sons, p. 356, ISBN 9781118031032.
  3. Faulkner, John R. (2014), The Role of Nonassociative Algebra in Projective Geometry, Graduate Studies in Mathematics, 159, American Mathematical Society, p. 13, ISBN 9781470418496.
  4. Dougherty, Edward R.; Astol, Jaakko (1999), Nonlinear Filters for Image Processing, SPIE/IEEE series on imaging science & engineering, 59, SPIE Press, p. 169, ISBN 9780819430335.
  5. Zill, Dennis; Wright, Warren S. (2009), Single Variable Calculus: Early Transcendentals, Jones & Bartlett Learning, p. 269, ISBN 9780763749651.
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