Answer:
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:
<u>x</u> <u>g(x)</u> <u> D1 </u> <u> D2 </u> <u> D3</u>
-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.