# Math Help - Classifying Function

1. ## Classifying Function

Let $f(x)=x^{x}$.

Is $f(x)$ a power function, exponential function, both or neither?

2. It is a power-exponential function.
That means it has higher order than an exponential function (it grows "faster" than an exponential).
I´m not quite sure if that´s how you say it in english, in highschool it was called "potencial-exponencial", an I tried to translate it as closely as possible.

3. So it's both? I don't completely understand why it should be both and not neither though; I wouldn't know how to explain this. I've never heard of this type of function before and I wouldn't know how to justify any of them.

Thanks a lot for your help!

4. Is this answer correct?

The function f(x)=x^x is neither a power function nor an exponential function. A power function has the independent variable as the root being raised to a fixed power, and an exponential function has a fixed number root being raised to the independent variable. By having the independent variable as the root and the exponent, the function is neither a power function nor an exponential function.