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Thread: Transformations

  1. #1
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    Exclamation Transformations

    Hi,

    When using the dash method for determining transformations, when it says a translation of +2 units parallel to the x axis, does this mean +2 units from the y axis?
    So would it be : (x,y) --> (x, y+2)?? Similarly to this, would a dilation of 2 parallel to the x axis, mean dilation 2 from the y axis? (x,y) --> (x, 2y) ?

    Could someone please clarify the use of the words parallel or from the x or y axis in regards to the use of this dash method.


    Thank you

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  2. #2
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    Re: Transformations

    Quote Originally Posted by ChanelSapphire View Post
    When using the dash method for determining transformations, when it says a translation of +2 units parallel to the x axis, does this mean +2 units from the y axis?
    So would it be : (x,y) --> (x, y+2)?? Similarly to this, would a dilation of 2 parallel to the x axis, mean dilation 2 from the y axis? (x,y) --> (x, 2y) ?
    It is a curse of mathematical terminology is that there is no international standard.
    The transformation $(x,y)\to(x,y+2)$ simply takes a graph two units up (a positive vertical transformation).
    Because the transformed graph "looks" exactly the same with respect to the x-axis but "moved" two units up, we would say that it is parallel to the x-axis.
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  3. #3
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    Re: Transformations

    Quote Originally Posted by Plato View Post
    It is a curse of mathematical terminology is that there is no international standard.
    The transformation $(x,y)\to(x,y+2)$ simply takes a graph two units up (a positive vertical transformation).
    Because the transformed graph "looks" exactly the same with respect to the x-axis but "moved" two units up, we would say that it is parallel to the x-axis.
    Thanks!!
    So for this question, would this be correct:
    (x,y) --> (x-1,4y+2) ?
    so x'= x-1 and y'=4y+2
    x= x'+1 y= (y'-2)/4
    so the transformed graph would be y = 4(x-1)^3 +2
    Is this the correct interpretation of translation parallel to the x and y axis?
    Transformations-screen-shot-2017-11-06-4.55.17-pm.png
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  4. #4
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    Re: Transformations

    Quote Originally Posted by ChanelSapphire View Post
    .
    Doing any sort of "bumping" does nothing but aggravate.

    Quote Originally Posted by ChanelSapphire View Post
    Thanks!!
    So for this question, would this be correct:
    (x,y) --> (x-1,4y+2) ?
    so x'= x-1 and y'=4y+2
    x= x'+1 y= (y'-2)/4
    so the transformed graph would be y = 4(x-1)^3 +2
    Is this the correct interpretation of translation parallel to the x and y axis?
    Click image for larger version. 

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    This particular subject has no universally accepted vocabulary. We have no way to know the background material given to you by the instructor/textbook. That is to say that we cannot give you a tutorial.
    I have a suggestion for a reference textbook that gives excellence coverage on transformations.
    Any good mathematics library should have Modern Geometries by James R. Smart.
    Last edited by Plato; Nov 6th 2017 at 09:23 PM.
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