# Power function

A power function is a function of the form:

Its domain is the set of non-negative real numbers .

Its codomain is also the set of non-negative real numbers .

The relationship between the swinging time and the length of a pendulum is, for instance, given by a power function.

## How does the constant a affect a power function?

0 < a < 1: The power function is growing with decreasing slope.

a > 1: The power function is growing with increasing slope.

a < 0: The power function is decaying.

a = 1: It’s a linear function.

a = 2: It’s a quadratic function.

If two points (x_{1},y_{1}) and (x_{2},y_{2}) are given, you can calculate the constant a with the formula:

## How does the constant b affect a power function?

The graph of a power function is passing through the point (1,b).

If the constant a and one of the graph’s points (x_{1},y_{1}) is given, it is possible to calculate the constant b:

## The multiply-multiply property of power functions

Given a power function of the form . According to the multiply-multiply property you will have to multiply the function by k^{a}, if you multiply x by the constant k:

For example: Given the function:

If the functions input is x=2, the outcome is 12:

Now we multiply x by 3, whereby we get the outcome 108:

Had we multiplied the result, 12, we got in the first place, by k^{a}= 3^{2}=9 instead, we would have achieved the same result:

## Calculate the constants a and b of a power function with two points given

Please enter the coordinates of two points.## Recognizing a power trend in a data set

If you have two sets of data, and you want to know if there is a power trend in the relationship between them, you can plot them within a coordinate system, both axes of which have logarithmic scales. The more the points fit to a straight line, the closer to a power trend they are.