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Transformation Matrices

  1. May 21, 2009 #1
    Hi

    I'm sitting for an AQA exam tomorrow (Pure Maths MPC2) and while going through some past papers I encountered this problem which I'm not sure how to solve. I'd appreciate any help :)

    1. The problem statement, all variables and given/known data
    i) Describe a single geometrical transformation that maps the graph of y=6^x onto the graph of y=6^(3x).

    ii) The graph of y=6^x is translated by the matrix [1; -2] (it is a 2x1 matrix) to give the graph of the curve with equation y=f(x) . Write down an expression for f(x).
     
  2. jcsd
  3. May 21, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    If you are taking an exam in these, surely you must know something! What have you tried?
     
  4. May 21, 2009 #3
    well, if i were doing the exam right now, for i) i'd say it would compress the x-axis
    however i'm pretty uncertain about (ii)
     
  5. May 21, 2009 #4
    while thinking about the second part I came up with two possible solutions which both seem right and ended up getting more confused

    you shift every (x,y) points by the vector [1 -2] (ie move one to the right and down two)
    or
    use the matrix transformation equation and end up with y=x-2*6^x
     
  6. May 21, 2009 #5

    Mark44

    Staff: Mentor

    After some thought, I think what this means is that each point on the graph of y = 6^x is translated one unit right and two units down. The description is a bit confusing in its description of the graph being translated by a matrix. Although [1 -2]^T is indeed a matrix, it might have been clearer to describe this as a translation by an amount represented by the given vector.
     
  7. May 21, 2009 #6
    Ok. I completely got it now. Thanks a lot for your help
     
  8. May 21, 2009 #7

    Mark44

    Staff: Mentor

    And BTW, this has nothing to do with transformation matrices, which you used as the title for this thread.
     
  9. May 21, 2009 #8
    Sorry about that. At the time I posted the problem I still thought that I needed to use the matrix transformation equation to solve it. The wording of the question confused me
     
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