BEGIN and END signs normally aren't used to mark the endpoints of supplemental roads in Missouri (although there are exceptions). On the west side of Mexico at the city limit on Liberty Street, Route FF begins. In this case, the state had put up a marker (left) to indicate the beginning of state maintenance, not normally done in conjunction with the first marker at the road's endpoint.
On the other side of the road (right) is the standard marker used to indicate the end of state maintenance.
Update: These photographs were taken in September 2002. When I drove by the same location in March 2003, the state maintenance marker had been removed from the Route FF sign post.