Whenever the route of any state highway passes through the corporate limits of any city of this state, the Department of Transportation:
(1) Shall select and designate the streets of the city over which the state highway shall be routed.
(2) Shall erect and maintain such road and other signs on and along such streets at such places and of such material and design as it may select.
(3) May alter or change such routing when in its opinion the interests of the motoring public will be better served.