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Homework Help: Did I get it wrong? (transformation problem)

  1. Jan 22, 2007 #1
    1. The problem statement, all variables and given/known data

    I just got back from writing my grade 12 math final and I figure I did really well. There was only one question that stumped me, and it was freaking stupid, too. So the problem was this:

    There was a picture of [tex]y=x^{3}[/tex] and the points P(2,8) was labelled. The question was where does the point P go if the graph is expanded horizontally by a factor of 3 about the line x=4... What the hell did they mean? I thought they meant that you first shift the graph over 4 places to x=4 and then you would apply the transformation, the point would end up being Q(10,8) but that wasn't even on there.

    Here were my choices...

    A.(8,8)
    B.(14/3,8) (I think)
    C.(10/3,8)
    D.(-2,8)

    I ruled out D pretty quickly and went with A... but it didn't make any sense. Did I get it wrong? :cry:

    Pretty sad the the only question that stumped me was a transformation question... :eek:

    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Jan 22, 2007
  2. jcsd
  3. Jan 22, 2007 #2
    Woops, I meant you would apply the transformation and then shift it over, wrong way around. But anyways, both methods were fruitless.
     
  4. Jan 23, 2007 #3

    HallsofIvy

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    Science Advisor

    I would interpret that to mean that the point's distance from x= 4 is multiplied by 3- if x is larger than 4, then it moves to the right 3 times that distance. If x is less than 4, then it moves to the left 3 times that distance.

    In this example, 2< 4 and the distance from 2 to 4 is 4-2= 2. (2, 8) is transformed to a point with x< 4 and 4- x= 3(2)= 6 so x= 4- 6= -2. Since the change is only horizontal, y does not change.
    (2, 8) is transformed to (-2, 8)

    How did you rule out D "pretty quickly"?
     
  5. Jan 23, 2007 #4
    That sounds like a good interpretation. Definitely makes sense to me now that I think about it. I figured that no positive stretch is going to result in a positive point moving to the left... But I was wrong!

    Thankyou for clearing that up, I understand the concept now.
     
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