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 (x1,y1) and (x2,y2) 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 (x1,y1) 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 ka, 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 ka= 32=9 instead, we would have achieved the same result:
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.