If you go to bed late do you feel you can't function properly?

Yes. Nowadays I always try to sleep at 10-ish (and get up for school at 6:00), but sometimes I get carried away with either a) homework, b) social media, or c) showering late with wet hair, and end up sleeping at 12-1:00am. I can get up, but halfway through the day I’ll find myself wanting to sleep in class or getting a head ache.

Rest is important in order to function properly or else you would have fatigue on your hands.

Depends on how much sleep I get.

Recent research shows that if you don't get enough sleep, it actually causes your neural network to slow down ... Meaning your thoughts and reactions are slower.