Take a look at the applet: Power Functions
If is directly proportional to a power of , so , then this is called a power function. The constant is called the proportionality constant.
You can look at a few examples of power functions here. In these functions, is always positive or and .
There are two ways to reverse the calculation in a power function (thus with ):
Depending on the value of you can get one or two values for x.
If the proportionality factor has a value other than , then you have to start with dividing by . From there you can either apply the root of power , or use the inverse power.
The rules for working with powers (see: "Exponential functions" ) are valid here, too!
For every and any real numbers en the following properties of powers and exponents apply:
as long as
as long as en .
as long as