Is #g(x) = (x^2 - 5)/(x^3)# a polynomial function and if so what is the degree?
This is a rational function
Having a polynomial in the numerator and the denominator (in such a way that they do not cancel out nicely) implies that you have a rational function.
You function has a polynomial of degree 2 in the numerator, and a polynomial of degree 3 in the denominator. These do not cancel out easily, and hence this implies that you have a rational function
Hope that helped :)