It is the Prime Minister's prerogative to appoint or dismiss a minister.

Function : an activity that is natural to or the purpose of a person or thing.
Monopoly : the exclusive possession or control of the supply of or trade in a commodity or service.
Authority : the power or right to give orders, make decisions, and enforce obedience.
Privilege : a special right, advantage, or immunity granted or available only to a particular person or group.
Prerogative : a right or privilege exclusive to a particular individual or class.

Synonym of Prerogative is Privilege