Question

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

Answer 1

Answer: $Degree=4$

Step-by-step 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:

$Degree=4$