If i have a very low tolerance to alcohol-does that mean i have a poorly functioning liver?

No.: The liver affects the length of time you stay drunk, not the amount you need to get drunk.

No: Some people are inordinately affected by alcohol, just as some are affected by tranquillizers or other medicines. Sometimes people who are very sensitive will look intoxicated after even a single drink, something called pathological intoxication. This sensitivity is from your brain and nervous system, nobody can explain it, and it is not likely anything to do with your liver.