No, because delta can't ever go below 0 or above 1, but it will be close to 0 for low prices (OTM options) and close to 1 for high prices (ITM options). So it'll always form a kind of S-curve.
Oh okay, makes sense. Can you share a resource where I can read up on this?
Natenberg wrote the classic tome on the subject (Option Volatility and Pricing) but the burned hand teaches best. Trade some options, lose some money, and you'll learn what to do and what not to do.
Delta for put options is typically below 0.
Sure, for put options it ranges between 0 and -1 for the same reasons, and the same argument holds for why gamma can't be constant.