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Math Help - Transformation of graphs question

  1. #1
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    Transformation of graphs question

    I have got a Graphing Test coming soon. And while preparing for the test, I came across this question that stumped me. The question is attached in this thread. The problem is, I am not sure how to transform a graph of f(1-x) into 1/f(1-x). Hopefully someone here can guide me along. Thanks in advance.

    P.S Is there any sequence while doing transformations? And when dealing with modulus functions should I mod the function first before doing the translations,scalings and reflections? Just want to get things clear before the test.


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  2. #2
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    Re: Transformation of graphs question

    start by plotting the reciprocal points of the known y-values of f(1-x) ... note that where f(1-x) = 0 , 1/f(1-x) will have a vertical asymptote; where f(1-x) has a vertical asymptote, 1/f(1-x) will equal 0. finish up by connecting the points by a smooth curve.

    y = 1 will still be a horizontal asymptote ... the graph of y = 1/f(x-1) will just approach it from the opposite side.
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  3. #3
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    Re: Transformation of graphs question

    So do you mean that you can't sketch this graph by applying scaling/translating/reflecting to the original graph? Because I don't really understand what you mean by plotting reciprocal points etc. But it could be because I haven't learnt it.

    Anyways thanks for your reply
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