Could you tell me If "to adults" is obligatory or not as in
I taught English to adults.
I was told in school that "to adults" is an indirect object.
I (S) + taught (V) + English (D.O) + to adults (I.O)
If that's obligatory, I would be attempted to call it as an adverbial complement modifying "taught".
I (S) + taught (V) + English (O) + to adults (Adverbial Complement)
But, I suppose "to adults" is just an adverb phrase. (not obligatory)
It seems to me that the removal of the prepositional phrase can't render the sentence ungrammatical. i.e., "I taught English." I perfectly understand.
I (S) + taught (V) + English (O) + to adults (Adjunct)
Best Answer
"I taught English" is a complete, correct sentence. "I taught English to adults" is also a complete, correct sentence.
Native speakers of English are likely to understand "I taught English" as equivalent to "I taught English to school-aged children", because that's the default assumption for anyone teaching anything. If you say either sentence in a country where English is the common tongue, native speakers will assume you mean you taught English literature and/or writing skills, not the language, because that's what the school course called "English" will focus on.
In comments on the other answer, you seem to be insisting on a grammatical distinction between a "complement" and an "adjunct". English is not a language whose constructions fall into well-defined categories with sharp edges. Prepositional phrases like "to adults", "on the table", etc are especially hard to categorize. I think it's easier to understand your examples in terms of the transitivity of their main verbs. English has at least five different transitivities for verbs:
I put the dish on the table: ditransitive. Subject, indirect object, and direct object are all required. You have to say what you put and where you put it. "On the table" is a prepositional phrase, but any locative construction will do.
I taught English: transitive. Subject and direct object are required. You have to say what you taught, unless it's clear from context. You can, again, add more information with prepositional phrases.
I ate [an apple]: ambitransitive. Subject is required, direct object is optional. You can say what you ate, using a direct object, but you don't have to. (Perhaps you only want to communicate that you're not hungry right now.)
I slept: intransitive. Only a subject is required. You have to say who slept, but no more words are required for a complete sentence. You can add more information with prepositional phrases, e.g. "at home", "on the train", "for only three hours".
It rained: impersonal. Not only are no object phrases required for this complete sentence, the "it" isn't a real subject. You can't leave it out, but it has no referent and you can't substitute any other subject phrase without sounding weird. (Many of the world's languages treat verbs describing weather this way.)
(It is not clear to me that any language's constructions fall into well-defined categories with sharp edges, but that's a whole 'nother can of worms.)