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Math Help - Transformation Questions! Please Help!

  1. #1
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    Transformation Questions! Please Help!

    I'm REALLY having trouble with these two questions!

    1. If the point (4, 5) is on the graph of y = f(x), the graph of y = f -1(x) - 9 will change this point so that the y-coordinate is...

    2. Thegraphof y = f(x) contains the point (6, -10). If y = f(x) is transformed to y = -4f(-6x - 15) + 15, the point (6, -10) is changed to the point (p, q). What are the values of p and q?

    Thank you SO much for the help, I really appreciate it.
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  2. #2
    Senior Member vincisonfire's Avatar
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    (i)  f^{-1} *is a reflexion with respect to the line  y=x . Therefore, a point (a,b) becomes (b,a).
    But here you have  f^{-1} -9 , so the symmetry acts and there is a translation of 9 in the negative y-axis direction.
    Therefore, a point (a,b) becomes (b,a-9).
    Last edited by vincisonfire; December 1st 2008 at 05:04 PM.
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  3. #3
    Senior Member vincisonfire's Avatar
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    If y = f(x) is transformed to y = -4f(-6x - 15) + 15
    then y=-4f(-6(x+5/2))+15.
    You see that the x-axis is compressed by a factor of 6, therefore, the point x=6 becomes the point x=1.
    Then it is translated by 5/2 to the left, and the point x=1 becomes the point x=-3/2.
    The function is scaled by a factor of 4 in y so the point y=-10 goes to y=-40.
    It is reflected (factor of -1) with respect to x-axis so the point y=-10 goes to y=40.
    It is translated of 15 unit upwards so the point y=40 goes to y=55.
    (6,-10) -->*(-3/2,55)
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