for part (a) you can call it a polynomial function.
for part (b): in general setting you would say that the domain is R. In this case, since t is in hours, then the domain is .
for part (c): the objective is to find the value of t for which f(t) becomes zero. This happens only if t=0 which is not a logical answer. There must be something wrong with the given. Take a look at this: http://www.wolframalpha.com/input/?i=t^5%2B3*t^4-6*t^3-2*t^2%2B60*t