What is the degree of the power function represented in the table? 1 2 3 4

Question

x
−2	−8
−1	−1
0	0
1	1
2	8

Answer 1

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

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

The third differences (D3) are constant, so it's a degree three polynomial.

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