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Translations math problem (gr 12 level)

  1. Dec 26, 2008 #1
    1. The problem statement, all variables and given/known data
    If the function y=f(x) is transformed to -2y-2=f(0.5x-3), and the point (-3, -2) is on f(x), which of the following will be on the new function -2y-2=f(0.5x-3)?

    2. Relevant equations
    [tex] y = {af}\left[b(x-h)\right] + k [/tex]

    3. The attempt at a solution
    When i attempted this question, i got (-9, -1) which is wrong, i don't know the answer still. I am still unsure really how to show my work so i pretty much did the horizontal translations and scale factors to x, and vertical translations and scale factors to y.

    after rewriting the function, i have [itex] y = -\frac{1}{2}(0.5x-3) + 2 [/itex]

    in an attempt to show work i showed the transformations.

    [itex]x \rightarrow 0.5x [/itex]
    [itex]x \rightarrow x - 3 [/itex]
    [itex]y \rightarrow 2y [/itex]
    [itex]y \rightarrow -y{}\textit{(reflection on x axis)} [/itex]
    [itex]y \rightarrow y - 2 [/itex]

    I then simply tried to run those transformations on the x and y values seperatly.
    (-3, -2)

    x = -3(2) -3 = -9
    y = -((-1/2)(-2)) + 2 = 1?? im lost,

    i dont really know how to show my owkrk for this question, nor how to do it properly.
    any help would be appreciated.
  2. jcsd
  3. Dec 26, 2008 #2
    This was also a multiple choice question. Possible answers were
    (-9, -1)
    (1, 0)
    (0, 0)
    (-12, 2)
  4. Dec 26, 2008 #3


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    Science Advisor

    Saying that "(-3, -2) is on f(x)" means that f(-3)= -2. In order that we be able to use that, without any other knowledge of f, we need to be able to apply f to -3 so would have to have 0.5x- 3= -3 so 0.5x= 0 or x= 0. In that case, we have -2y- 2= f(-3)= -2 so -2y= 0 and y= 0. The point is (0, 0).
    Last edited: Dec 26, 2008
  5. Dec 26, 2008 #4
    wow, i feel really really dumb, makes sense putting it that way.. looked at it on a graph, was able to do it that way, algebraically i wasn't able to see it like that.. so its easy, transformation applied to x = previous x value? i dont understand why you cant sub -3 in for x and use that to transform it though, sorry for being all dumb about it...

  6. Dec 28, 2008 #5
    That's not right. What happened to the f? If the function [tex]y = f(x)[/tex] is transformed to [tex]{-}2y{-}2 = f(0.5x{-}3)[/tex], then
    [tex]y = {-}\frac{1}{2}[f(0.5x{-}3)] {-} 1[/tex].

    But you don't need to do this at all; HallsofIvy's solution is the way to go.

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