Entertain: pretty much every fictional text falls into this category. Whether it be a story, poem, or play, if it is a product of the imagination, then it was probably written to entertain. Of course, this category could also include texts like television scripts, books full of knock-knock jokes, and comic books.
Inform: texts that provide information about a topic were written to inform. Some examples include encyclopedia entries, newspapers, recipes, instructions, biographies, and the nutrition facts on the back of food products.
Persuade: if the speaker is attempting to influence or convince the reader of some idea, then the text was probably written to persuade. Some examples of persuasive texts include campaign speeches, advertisements, and persuasive essays.