Horizontal translation

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. A graph is translated k units horizontally by moving each point on the graph k units horizontally.

For 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.

If function transformation was talked about in terms of geometric transformations it may be clearer why functions translate horizontally the way they do. When addressing translations on the Cartesian plane it is natural to introduce translations in this type of notation:

or

where and are horizontal and vertical changes respectively..

Example

Taking the parabola y = x2 , a horizontal translation 5 units to the right would be represented by T((x,y)) = (x + 5, y). Now we must connect this transformation notation to an algebraic notation. Consider the point (a.b) on the original parabola that moves to point (c,d) on the translated parabola. According to our translation, c = a + 5 and d = b. The point on the original parabola was b = a2. Our new point can be described by relating d and c in the same equation. b = d and a = c  − 5. So d = b = a2 = (c − 5)2 Since this is true for all the points on our new parabola the new equation is y = (x − 5)2.

gollark: ```You can make an account on any Mastodon instance and interact with users on this or any other one. That being said, here's reasons why you should choose this instance: You like stellated platonic solids very much. You think our rules make a lot of sense. You want to try out Mastodon / being on The Fediverse, this place being as good as any other instance for that. You think, correctly, that @halcy or @dotUser are exceedingly good at online.```
gollark: Of course somebody made `icosahedron.website`.
gollark: "I will join a technically interesting social network which nobody uses so I can talk to nobody."
gollark: It sounds like a very hydraz sort of thing to do.
gollark: I was looking at running an instance, but didn't bother to.

See also

References
    • Zazkis, R., Liljedahl, P., & Gadowsky, K. Conceptions of function translation: obstacles, intuitions, and rerouting. Journal of Mathematical Behavior, 22, 437-450. Retrieved April 29, 2014, from www.elsevier.com/locate/jmathb
    • Transformations of Graphs: Horizontal Translations. (2006, January 1). BioMath: Transformation of Graphs. Retrieved April 29, 2014


    This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.