Question

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?

Answer 1

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

`f(x)=kx^p`

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.