Answer:
There are more than 3 possible purposes for a document, but I will stick to the 3 main that I think will fulfill your answer.
The 3 purposes for a document would be to inform an audience, to list an order of steps or directions (some type of chronological ordering), or to persuade an audience.
For an informational document, I would suggest a news article or some type of news-related document where the writer is using the document to inform a given audience.
For an ordered/chronological document, I would say experiment documents, (in subjects such as chemistry) in which there is a list of steps or orders in which the reader should follow. Another example would be recipe cookbooks but cookbooks are a little informal to use.
Lastly, for a persuasion-related document, business proposals are the perfect example for persuaing an audience to think a certain way. Business proposals allow for a layout of solutions to a problem in relation to the business and backs up the proposal with a list of reasons to why the solutions given are the best solutions that can be offered.
I hope I solved your question!