I would say that a persuasive essay would have those elements.
After thinking about the other types of essays, a narrative tells an entertaining story (not meant to give information), an expository tries to explain information in an unbiased way, and a descriptive essay is similar to a children's book with specific details and whatnot.
A persuasive essay tries to convince the reader to believe what the writer wants him/her to believe whether it appeals to emotions, reason, or facts.