Final answer:
The parentheses provide the years Franz Joseph I reigned, which is contextual information separated from the main sentence flow.
Step-by-step explanation:
The parentheses in the sentence "The Hapsburg rule of Austro-Hungarian Empire effectively ended with the reign of Franz Joseph I (1848 - 1916)." serve to set off useful information that does not fit directly into the flow of the sentence.
In this case, the purpose of the parentheses is to provide additional context to the reader, specifying the years that Franz Joseph I reigned over the Austro-Hungarian Empire. This information helps the reader understand the time period during which Franz Joseph I ruled, but it is not the main focus of the sentence, hence it's separated by the parentheses.
The purpose of the parentheses in the statement "The Hapsburg rule of Austro-Hungarian Empire effectively ended with the reign of Franz Joseph I (1848 - 1916)" is to set off useful information that does not fit directly into the flow of the sentence.