exponents on functions and their effects.

I've been somewhat curious about how exponents really do effect functions. Linear functions are always changing at the same rate, while parabolas take more time to pick up, but eventually change at a very quick rate. But what about when y=x^3 or y=x^4 and so on? well I decided to get some geogebra help on this one. This is what I found...

All these functions meet at the same point, at (1,1). Also, we can see that before x=1, the functions with the higher exponents have lesser y values, and after x=1 it's the opposite. One last thing, all functions with odd nuber exponents penetrate the 3rd quadrant, while the functions with even number exponents penetrate the 2nd.

idk, I kind of found this interesting, what do you think?