Question

f(x)=6x^3+5x^2...is this a function, if so what is the domain and range

Answer 1

Set the function equal to zero and solve.
You can factor out to get two functions
\[x^2(6x+5) = 0\]
\[x^2 = 0\] and \[6x+5 = 0\]

Answer 2

You can put any number in and get a new one with your formula.
So now you already know two things: yes it's a function and the domain is all real numbers.
@abbot: knowing the the zeroes is nice, but of no importance if it's a 3rd degree function.
Think about what the range can be: there might be some wiggling going on around the zeroes, but as x grows very large (pos or neg), so does f(x)!
You now also know the range...