
sine function transforms
hello
say i have two functions, $\displaystyle y=3^x$ and $\displaystyle y=x+1.2$ and i wanted to find where they intersect. since $\displaystyle y=x+1.2$ is a line, if i could rotate both functions so that $\displaystyle y=x+1.2$ became the xaxis, $\displaystyle y=0$, then to find the intersection i would solve the now rotated $\displaystyle y=3^x$ by setting $\displaystyle y=0$, then unrotating the solutions.
firstly, how can i accomplish this rotation transform, and secondly, can i do more complex transforms, like $\displaystyle y=2^x$ and $\displaystyle y=x^2$ transformed so that $\displaystyle y=x^2$ becomes the xaxis? again, i would also have to detransform 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 $\displaystyle x^2$ and rotating each one into $\displaystyle y=0$ as in the first case.
and for the real kicker (or maybe you'll just kick me), how about $\displaystyle y=sin(\pi*2^x)$ and $\displaystyle y=sin(\pi*2^{1x})$? ..and again, detransformation.
*edit*
transforming certain functions would cause the other to no longer be a function..not a good idea haha.
but,
given the range $\displaystyle 0<x<1$ could these last functions be modeled by a polynomial?
thanks for any help or ideas!