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Math Help - Invariant - fixed point.

  1. #1
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    Question Invariant - fixed point.

    question is

    the graph y=(x-2)^{2}-1 represents y=f(x). What are the coordinates of the points that would be invariant for the transformations?
    then it has a list of 5 equations to find these points for.
    Last edited by brentwoodbc; February 17th 2009 at 12:06 PM.
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  2. #2
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    I think you're a little on the wrong track here. A fixed point is one that doesn't change after a transformation. Consider this simple example f(x)=x and the transformation f --> f^2. What points are fixed? In other words what values of x satisfy f(x)=f^2(x). The solution is fairly simple:

    f(x)=f^2(x)

    x=x^2

    x=0 or x=1.

    Now let's look at your problem:

    The transformation is f --> -f, so:

    f(x)=-f(x)

    2f(x)=0

    f(x)=0

    (x-2)^2-1=0

    Solve that and you'll have your answer.
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