Power functions > Powers
12345Powers

Theory

Take a look at the applet: Power Functions

If y is directly proportional to a power of x , so y = c x p , then this is called a power function. The constant c is called the proportionality constant.

You can look at a few examples of power functions here. In these functions, p is always positive or 0 and c = 1 .

There are two ways to reverse the calculation in a power function y = x p (thus with c = 1 ):

  • x = y p

  • x = y 1 p

Depending on the value of p you can get one or two values for x.
If the proportionality factor has a value other than 1 , then you have to start with dividing by c . From there you can either apply the root of power p , or use the inverse power.

The rules for working with powers (see: "Exponential functions" ) are valid here, too!

For every x and any real numbers a en b the following properties of powers and exponents apply:

  • x 0 = 1

  • x - a = 1 x a as long as x = ! 0

  • x 1 a = x a as long as x 0 en a > 0 .

  • x a + b = x a x b

  • x a - b = x a x b as long as x = ! 0

  • ( x a ) b = x a b

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