In a supervisor system, a board of supervisors is responsible for

governing the county, overseeing departments, and creating policies.

governing the county, with little power to create policies.

governing the county with a council and an executive.

governing the county, creating policies, and supervising a council ...

The Board of supervisors has the executive power (governing the country, creating policies and overseeing departments - the last one is true at least in Los Angeles) but it also has legislative powers and even some judicial powers ...

So the correct answer is: governing the county, overseeing departments, and creating policies.