1
$\begingroup$

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

x^2

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

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?

  • 0
    @anorton Ah ha! That makes complete sense.. Thank you2012-11-05

2 Answers 2

0

My mistake. 0.9^200 does not equal 7.05. From the calculator, it says 7.05.. x 10^-10. The 10^-10 represents places in the tenths, hundredths, etc. So 0.9^200 does not equal 7.05... but in fact some ridiculously long decimal number in a "-ths" place I can't find a name for.

  • 1
    @anorton you're awesome2012-11-06
0

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 $x < 1, n >= 1$