Finding a codomain with little information

Question

We have been specifically asked to write out the entire codomain for various basic functions such as 7x + 11 with the domain {0, 1, 4, 9} And other linear functions with small domains.
Surely the codomain would just be all real numbers, but we can't just write R

Has my lecturer finally lost it, or am I missing some fundamental understanding?

EDIT: The whole lecture was about Images and Codomains. He wanted us to write out both the Image for the given domain as well as the Codomain. :D It wasn't a slip of the tongue either, it was written in the presentation as well. Regardless, I guess it's just a folly on my lecturer's behalf.

Answer 1

Presumably by codomain they meant the image of the function, because otherwise it wouldn't make sense to ask such a thing. The image consists of all points which are mapped to by the function.

Answer 2

I suspect that your lecturer wants you to find the image of those functions. You are right that technically the codomain can be basically anything, as long as it contains the image. It could be just the image, or it could be $\Bbb Z$, or $\Bbb R$ or something even larger, or anything in-between.

Whther you should point that out to him or just give the answer that he wants depends very much on how well you kow him. But if you do give the answer $\Bbb R$, then I recomment that you do it with careful explanation, preferably rooted in the definition of codomain as given by your book / lecture notes (if available), and not by Wikipedia or strangers on an internet forum. That is probably the best way to legitimize your claim that you have, in fact, given a correct answer and not just written down some random, relevant-looking symbol.