In addition to the duties set forth elsewhere in this part, the board shall do all of the following:
(1) Advise the governing body on matters of personnel administration, including the development of personnel rules, a job classification plan, and a systematic pay plan.
(2) Represent the public interest in the improvement of personnel administration in the city service.
(3) Make any inquiry which it may consider desirable concerning personnel administration in the city service.
(4) Make recommendations to the governing body with respect to any of the foregoing duties.