My mother is now back with us.
Does "back" in the sentence function as an adverb? Can adverb phrase function as subject complement?
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My mother is now back with us.
The phrase back with us is a preposition phrase. It is headed by the preposition back. The Original Poster asks if back can be considered a subject complement. It does indeed describe the subject, my mother. Because it tells us the location of my mother, we call it a locative complement.
We often use preposition phrases as locative complements:
We can show that back is a preposition and not an adverb. The Original Poster asks whether adverbs can function as Subject Complement. The answer is that adverbs can NOT normally function as complements of the verb BE - but prepositions and preposition phrases can:
Adverbs as complements of BE
Preposition Phrases as complements of BE
Also, adverbs can't usually modify noun phrases. Prepositions and preposition phrases can:
Adverbs modifying nouns
Preposition Phrases modifying nouns
In addition, adverbs can usually be modified by the adverb very, prepositions usually cannot:
Adverbs modified by very
Prepositions modified by very
Lastly, most prepositions and preposition phrases can be modified by the special adverbs straight and right. Adverbs cannot usually be modified by straight or right:
Adverbs modified by straight or right
Prepositions modified by straight or right
The Original Poster's question
In the Original Poster's example the preposition back has another preposition phrase as its complement. The complement of the preposition back is with us. This second preposition phrase has the preposition with as its head. The complement of with is the pronoun us. The whole preposition phrase back with us functions as the complement of the verb BE. It is a locative complement telling us the location of the subject, My mother.
Adverbs, on the other hand, do not usually function as complements of the verb BE. We do not usually find them, therefore, as subject complements.
Hope this is helpful!
In your sentence, 'back' is being used as an adverb of place. I think the issue here is that 'Mother' (a person) cannot equal 'back' (a location). You can't have a 'back mother.' That is nonsense.
But an adverbial phrase CAN be a subject complement. I'll throw this out:
You have to be smarter than the horse you are riding.
In this example, 'smarter' is a complement to the subject, 'you.' The two are equivalent. In this case, 'You' (a person) can equal 'smarter' (an adjective). A big man. A yellow horse. These are possible. A 'smarter you' is also completely possible.
'Smarter than the horse' also happens to be an adverbial phrase of comparison. 'Than' is a correlative conjunction, connecting the grammatically equal 'you' and 'horse.' So the phrase 'smarter than the horse' becomes -- as a whole -- a subject complement. And it is an adverbial phrase. Behold, the two are one.
But I can't leave something unfinished. So:
'You are riding' has an elided 'that,' making it a non-defining relative clause.
I believe 'to be' is an infinitive direct object to 'have,' though some might consider 'have to be' a complex verb. For me, it is easier to think of infinitives as a discrete units functioning in specific ways instead of tacking them to whatever happens to be close by.
Yes, an adverb can also function as a subject complement in some cases. The word "back" in the sentence "My mother is now back with us" has been used as an adverb.
Cambridge English Grammar Today states:
"Subject complements can be adjective phrases, noun phrases, adverb phrases or prepositional phrases. I am upstairs (subject + adverb)".