You’ll not see nothing like the Mighty Quinn
None of those answers is right, but I can understand why thoughtful but imperfectly informed person might offer them. The FTC (and other regulatory agencies) can issue regulations that look a lot like laws and judicial decisions even though it’s not a legislative body or a court and even though it’s implementing and enforcing laws, which is an executive branch function.
I don't think the sort of person who knows what the FTC is would be the sort of person who would not be able to correctly answer the 'What are the three branches of the Federal government?' question. This isn't an example of 'being smarter than the questioners'....the three branches are fairly well defined in the constitution...they all just sometimes end up doing 'the wrong things'.
If someone said 'Define the three branches and their role in the government', yeah, some smart people might overthink the question and explain how the executive makes a bunch of rules, or how the courts often end up basically making laws, or at least regulations, if the laws are silent, but just the existence of the three branches and their names isn't in dispute.
OTOH, it does seem likely that some people said 'The president, Congress, and the Supreme Court', which is a) technically incorrect on every one of those, and b) entirely right in any meaningful sense, they just named the 'heads' instead of the branches.
Weirdly, if you look at the constitution, it might be possible to logically infer that the state governments, in a way, are supposed to be the fourth branch. I mean, they are Article 4, coming after legislative, executive, and judicial.
However, this falls apart if you keep going to Article 5, because 'How to amend the constitution' is a pretty abstract concept for a branch of the government, and they just get weirder.
Of course, if you read the actual text of the constitution, it doesn't name the branches what we call them anyway. E.g., it basically asserts that executive power _exists_, presumably as some sort of law of physics or something, and then _vests_ that power to Congress. The word 'branch' doesn't even appear in the constitution except for the obscure rule that members of the House of Representatives (And now the Senate) have to meet their own state's congress's most numerous branch of legislature requirements, a rule I literally had never heard of until this very post.(1)
1) A rule which, now that I think about it, appears to make a state imposing a Congressional term-limit legal. All a state would have to do is assert that someone cannot be elected to their state's Congress if that person has previously served X years in the US Senate, and, tada, they also cannot be re-elected to actual US Senate either. I don't know why no one's done this. Wow I'm off topic, but whatever.