All officers and members of boards and commissions of the city holding elective or appointive office on the effective date hereof, shall continue in office, and in the performance of their duties until the respective terms for which they were elected or appointed shall have expired and any such office which is discontinued by this charter shall thereupon be abolished. The powers which are conferred and the duties which are imposed upon any officer, commission, board or department of the city under general law, or under any ordinance or contract of the city in force on the effective date hereof, shall, if such office, commission, board, or department is abolished by this charter, be thereafter exercised and discharged by the officer, commission, board, or department upon whom are imposed corresponding functions, powers, and duties by this charter or by any ordinance or resolution of the council thereafter enacted.