Is this an error in this problem?

This problem seems to have an error, I think I've done it correctly but this is a chance for you guys to possibly prove a text book question wrong.

The problem is as follows:
One of the following tables of data comes from a linear function, one from an exponential function, and one from a non-linear polynomial function. Which one is the non-linear polynomial function?

x   -2 -1 0 1 2
f(x) 8  2 0 2 8

x      5  10  15  20  25
g(x) –13 –23 –33 –43 –53

x    -3 -2 -1 0  1
h(x) –3  0  1 0 –3

g(x) is easily deducted to be the linear, but between the non-linear polynomial function I am lost.

h(x) I have been able to find that it has an equation of -1(x+1)^2+1, thus meaning it is the polynomial. I would assume this is the correct answer, but it unsettles me that f(x) does not even appear to be an exponential function, but rather appears to be the power function 2x^2. Is this question erronous then?

Am I just overthinking this? Thanks for any input this is driving me crazy.

A TEXTBOOK WITH A MISTAKE? THAT'S UNPOSSIBLE!

Any finite set of points can be modeled with a polynomial, so both h and f could be polynomials.  The idea is to figure out which could be "exponential" as well.  That will depend on how exactly your book defines an "exponential function".  Clearly none of them have the form a*b^x, which is what my idea of an exponential function is.