She's a teacher working at a public high school. Now, you can say either of these:
(1) She teaches at a public high school.
(2) She works at a public high school.
Is the prepositional phrase "at a public school" a complement or an adjunct in (1)? How about in (2)?
This site shows this sentence:
Dr. Sneeden teaches English at the University of Florida.
And they say "at the University of Florida" is an adjunct.
And while I was looking at Oxford Modern English Grammar the other day, I came across a sentence similar to (2) with the verb "work".
I work in the Physiology Department.
And the book says "in the Physiology Department" is not an adjunct but a complement, because if the PP is left out the meaning of the sentence changes.
So I guess, according to these references, the PP in (1) is an adjunct and the one in (2) is a complement. If so, I'm still not sure why leaving out the PP from (2) changes (2)'s meaning but leaving out the PP in (1) doesn't change (1)'s meaning.