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Math Help - sine function transforms

  1. #1
    Junior Member pinion's Avatar
    Joined
    Jan 2008
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    sine function transforms

    hello

    say i have two functions, y=3^x and y=x+1.2 and i wanted to find where they intersect. since y=x+1.2 is a line, if i could rotate both functions so that y=x+1.2 became the x-axis, y=0, then to find the intersection i would solve the now rotated y=3^x by setting y=0, then un-rotating the solutions.

    firstly, how can i accomplish this rotation transform, and secondly, can i do more complex transforms, like y=2^x and y=x^2 transformed so that y=x^2 becomes the x-axis? again, i would also have to de-transform the solutions. if i was at all fluent in calculus (took 4 semesters worth of it, haha, just don't remember much), then i'm sure i'd have a better idea on how to figure this out, or at least ask better questions.

    *edit*
    for this one, i visualize flattening out one curve, and the other one obeys the same movements. mathematically i think it would be taking lines perpindicular to x^2 and rotating each one into y=0 as in the first case.

    and for the real kicker (or maybe you'll just kick me), how about y=sin(\pi*2^x) and y=sin(\pi*2^{1-x})? ..and again, de-transformation.

    *edit*
    transforming certain functions would cause the other to no longer be a function..not a good idea haha.
    but,
    given the range 0<x<1 could these last functions be modeled by a polynomial?

    thanks for any help or ideas!
    Last edited by pinion; February 2nd 2008 at 05:36 PM.
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