You can also fine-tune the feel of a jump when you're directly editing a handful of values vs trying to find a function that describes your desired results.
When you edit one coefficient of a polynomial, you change its behavior everywhere. When you change one value in a lookup table, you're only changing the value for one point in time.
i'd say a lookup table is more easily edited than a parameter in a function (provided that you are editing a function with less parameters than the entries in the lookup table).
