Question

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

Answer 1

Since the function is even, its degree must be even (so it might be 2, 4, 6, ...)

In particular, all these numbers are one more than a perfect fourth power:

$(-3)^4=3^4=81 \implies f(-3)=f(3)=81+1=82$

$(-2)^4=2^4=16\implies f(-2)=f(2)=16+1=17$

$(-1)^4=1^4=81 \implies f(-1)=f(1)=1+1=2$

$0^4=0 \implies f(0)=0+1=1$

So, the function is

$f(x)=x^4+1$

and the degree is 4.