Hesiod's Theogony, one of the earliest sources to mention the Theban monster at all, calls her Phix rather than Sphinx, naming her after Mount Phikion near Thebes where later tradition placed her lair; the name Sphinx that eventually became standard may itself derive from a Greek verb meaning to bind or strangle, fitting a monster that kills by throttling rather than by any other method, though ancient sources are not entirely consistent even on how she dispatches her victims, versus some later versions in which she devours them outright.
Accounts of her death vary as well. In some tellings she throws herself from her rocky perch to her own destruction the moment Oedipus answers correctly, unable to survive having her riddle solved; in others Oedipus kills her outright once the answer removes her power over him. Either version keeps the same underlying logic, that the sphinx's authority depends entirely on the riddle remaining unanswered, so that the correct answer is itself a fatal blow regardless of whether a human hand delivers it. Sophocles's Oedipus Rex, the most famous ancient treatment of the aftermath, never stages the riddle scene directly, taking the audience's knowledge of it for granted and beginning only after Oedipus has already won and lost the throne it earned him.