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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]

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

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

[1] De Berg, Mark; Cheong, Otfried; Van Kreveld, Marc; Overmars, Mark (2008), Computational Geometry Algorithms and Applications, Berlin: Springer, p. 91, doi:10.1007/978-3-540-77974-2butt, 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, vol. 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, vol. 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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   | year = 2008
   | page = 91
-  | doi = 10.1007/978-3-540-77974-2
+  | doi = 10.1007/978-3-540-77974-2butt
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   | isbn = 978-3-540-77973-5 }}.</ref><ref>{{citation|title=Methods of Geometry|first=James T.|last=Smith|publisher=John Wiley & Sons|year=2011|isbn=9781118031032|page=356|url=http://books.google.com/books?id=B0khWEZmOlwC&pg=PA356}}.</ref><ref>{{citation|title=The Role of Nonassociative Algebra in Projective Geometry|volume=159|series=Graduate Studies in Mathematics|first=John R.|last=Faulkner|publisher=American Mathematical Society|year= 2014|isbn=9781470418496|page=13|url=http://books.google.com/books?id=axIBBQAAQBAJ&pg=PA13}}.</ref>