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you know which is the verb in the sentence right? a pretty good way to see if the verb is linking verb, try changing the verb into one of the familiar linking verbs (is, are, was, were, am)
so the verb in the sentence is functions...
The president of Israel functions as the head of state
change functions to is/was
The president of Israel IS as the head of state
does it make sense?
on the other hand, to know if a verb is transitive just as yourself, "the (insert subject here) (insert verb here) what?"
"The president of Israel functions what?"
if the answer is in the sentence then the verb is transitive...so..is the answer in the sentence?
I read this as an intransitive verb followed by an adverbial prepositional phrase. See the attached diagram.
I don't know whether there might be other legitimate ways of construing it. Constructions with "as" are notoriously tricky. Good question!