if i understand what u want is how to diffreniate between diff. types ,for that by simple qualitative analysis is putting the s=0 for low frequency and s=inf for high freq.
for example:
1-LPF: s=0 gives a constant while s=infinity gives zero which is how a LPF acts.
2-HPF: s=0 gives zero while s=inf. gives constant (i.e. HPF)
3-BPF: s=0 gives zero also s=inf gives zero which means band pass.
4-BSF: s=0 gives constant and s=inf gives constant which means band stop.