A unit of local government may enter into a written agreement with any other unit or units of local government for the performance of any or all functions and activities that a party to the agreement, its officers or agencies, have authority to perform. The agreement may provide for the performance of a function or activity:
(1) By a consolidated department;
(2) By jointly providing for administrative officers;
(3) By means of facilities or equipment jointly constructed, owned, leased or operated;
(4) By one of the parties for any other party;
(5) By an intergovernmental entity created by the agreement and governed by a board or commission appointed by, responsible to and acting on behalf of the units of local government that are parties to the agreement; or
(6) By a combination of the methods described in this section.