# Power functions and parabola issue

With the function f(x)=x^2 we get a graph like so...

The rule for power functions, that I've been told, is the larger the power gets, the closer the line will touch the x-axis.

Example for f(x)=x^10

My understanding the reason this is, is because no matter how many times you multiply 1/-1 you will always get 1 for the output. So you should always have the parabola curving vertically right at -1/1. That part makes complete sense.

My question is, when you multiply 0.9^200 it equals 7.05...

So, the input 0.9 and output 7.05.. do not seem to stay within the parabola because the parabola doesn't start going vertical till it hits -1/1 on the x-axis..

Am I seeing this right?

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$0.9^{200}\not=7.05$ Rather, $0.9^{200} = 7.05\times10^{-10}$ – apnorton Nov 5 '12 at 23:53
See here: .9^200 – amWhy Nov 5 '12 at 23:55
@anorton so 7.05 x 10^-10 is not greater than 1? I don't understand how to read 10^-10 – Tyler Zika Nov 5 '12 at 23:55
10^(-10) = 0.00000000001 – apnorton Nov 5 '12 at 23:57
@anorton Ah ha! That makes complete sense.. Thank you – Tyler Zika Nov 5 '12 at 23:59

Ok. The reason the graph of $y=x^n$ (where $n$ is an even integer) starts to "hug" the x axis for a greater distance as $n$ increases is that multiplying two numbers less than one returns a smaller value.
Essentially: $$x^n < x$$ if $x < 1, n >= 1$