Question

The table shows ordered pairs for a polynomial function, f. What is the degree of f?

Answer 1

Answer:
`Degree=4`

Explanation:

In order to find the degree of the power function represented in the given table, you must find the difference of the y-values (values of f(x)) until they diferences are constant.

1) First differences:

`8-63=-55\\-1-8=-9\\0-(-1)=1\\-1-0=-1\\8-(-1)=9\\63-8=55`

2) Second differences:

You must find the differences between the First differences. Then, you get:

`-9-(-55)=46\\1-(-9)=10\\-1-1=-2\\9-(-1)=10\\55-9=46`

3) Third differences:

You must find the differences between the Second differences. Then, you get:

`10-46=-36\\-2-10=-12\\10-(-2)=12\\46-10=36`

4) Fourth differences:

You must find the differences between the Third differences. Then, you get:

`-12-(-36)=24\\12-(-12)=24\\36-12=24`

You can notice that the fourth differences are constant. This means that the degree of
`f` is:

`Degree=4`