# How to tell which function affect behavior of a function the most?

The problem that got me thinking. $\left(\dfrac{\sin x}{x}\right)^2$

The overall pattern of this function is a parabola but it has been pulled down by $1/x$ and it wobbles because of $\sin x$.

So, in general is there any mathematical method/way to determine which function is the most dominate?

so for any $\left(f\left(g\right)\right)^{h}$ how could I tell which function $f,g,h$ will affect the shape of the graph most?

-
This seems to really depend on $f,g,h$ to give anything general –  Belgi Mar 6 '13 at 1:15

Last but not least: if you pick a function $\psi$ it is very unlikely that it has a unique representation $\psi=(f\circ g)^h$...
I am not saying that your question is not high quality :) I'm just saying that such a general method does not exist. Imho all you can do is to analyze each case of the representation $(f\circ g)^h$ separately. –  Godot Mar 6 '13 at 2:04