The board of supervisors of a county that is only included in part within the south coast district may, by resolution, request the south coast district board to have that area of the county not included within the South Coast Air Basin included in the south coast district, or the board of supervisors may request to contract with the south coast district to perform air pollution control functions in that area of the respective county not within the South Coast Air Basin. The south coast district board may, by resolution, agree to (1) have that area of the county not included within the South Coast Air Basin included in the south coast district, or (2) perform air pollution control functions for that area of the county not included within the South Coast Air Basin, or both (1) and (2).