(1) record all proceedings of the county legislative body;

(2) make full entries of all resolutions and decisions of the county legislative body on all questions concerning the county;

(3) record the vote of each member on any question upon which there is a division;

(4) prepare and certify duplicate lists of all claims, showing the amount and date of each claim or order and the date of the allowance or rejection of the claim, which lists shall be countersigned by the county executive;

(5) deliver to and leave with the county auditor one of the lists referred to in Subsection (4) and deliver to and leave with the county treasurer the other list;

(6) file and preserve the reports of the county officers to the county legislative body;

(7) preserve and file all accounts acted upon by the county legislative body, except such as are necessarily kept by the auditor;

(8) preserve and file all petitions and applications for franchises, and record the action of the county legislative body on them;

(9) authenticate with the clerk's signature and the seal of the county the proceedings of the county legislative body if the proceedings are ordered published;

(10) authenticate with the clerk's signature and the seal of the county all ordinances or laws passed by the county legislative body, and record them at length in the ordinance book;

(11) record all orders levying taxes;

(12) keep at the clerk's office all county books, records, and accounts that the clerk is required by law to keep and keep them open at all times during regular business hours for public inspection; and

(13) perform all other duties required by law or by any rule or order of the county legislative body.