How do you determine the degree of a power function from a table? when do you know you have successfully determined the degree of the power function?

A power function is a function that can be represented in the form

where k and p are real numbers, and k is known as the coefficient.

Example:

f(x)=1    constant function.

f(x)=x     identity function

f(x)=x^2   quadratic function.

1)

we use the method of differences, g(x+1)-g(x). Keep taking differences until they are all constant.

for example:

if we have a set of values as:

 x         g(x)

−2       −8

−1       −1

 0        0

 1        1

 2        8

Now when we find the difference as:

x       g(x)          D1              D2                     D3

-2       -8

-1         -1        1-(-8)=7

0          0       0-(-1)=1          1-7=-6

1            1       1-0 = 1           1-1=0               0-(-6)=6

2           8       8-1 = 7          7-1=6               6-0 = 6

As D3 is constant hence, the degree of the power function is 3.

2)

When we get a constant difference in the table of the difference method we will successfully get our degree.