I am learning to distinguish between rational and polynomial functions. A questions reads:
"State whether the function is a polynomial, a rational function(but
not a polynomial), or neither a polynomial nor a rational function. If
the function is a polynomial, give the degree."
g(x)= [x^2 - 2x - 8] / [x + 2]
I know that the top tier is a polynomial of degree 2 and the bottom tier is a polynomial of degree 1. By definition, a rational function is a polynomial divided by a polynomial where the lower tier cannot equal zero, which is what I seem to have here.
Since the function is rational, I do not have to give the degree, but can rational functions have a degree? Yes or no? If so, how would I calculate it.