There is no relationship between the number of spells you know and the number of spell slots you have.
As a third level ranger, you will have 3 spaces for spells.
As a third level ranger, you will have 3 known spells.
As a third level ranger with an XGtE archetype, you'll know an additional spell based on your class function (for example, Monster Slayer Magic).
Knowing a spell, regardless of whether it comes from standard class features (i.e. spell casting) or an archetype feature (e.g., Monster Slayer Magic), does not change the way you cast it (since they are still considered spells of rangers in any case). Just say (XGtE, p. 43):
(…) you learn an additional spell when you reach certain levels in this class, (…) The spell count as a ranger spell for you but it doesn't count against the amount of ranger spells you know.
It does not say that it grants an additional spell space, just an additional spell. He says he doesn't count against him number of spells you know (which is simply said not to "use" what would otherwise be the choice of a player's spells), but otherwise counts like a ranger spell, which means that it is subject to how ranger spells work according to your Spellcasting function, which means that it requires spending spell spaces. From Spellcasting (PHB, p. 91):
To cast one of these spells, you must spend a spell space of the spell level or higher.