Is there a limit to the number of tiles a city can work? I've noticed that I can purchase and use tiles several spaces away from my city. How far can I go?
Tiles up to three away from the city center can be selected to be worked.
Additionally, the number of citizens is the limiting factor for worked tiles. Let's assume a newly settled city has one citizen. Even if you buy tiles for that city, only one tile will be worked since the city only has one citizen.
Do note, however, that tiles that are not being worked on can provide adjacency for worked tiles. So buying/improving land that you cannot immediately(or in case of 4 space away, ever) work on can be beneficial, thou the return is significantly reduced. Furthermore, strategic/luxury resource does not need to be worked on to provide you the resource, so improvements on those are good anytime and any distance away.
Just like in Civ V, the maximum distance that can be worked is 3 tiles away from the city center.