What's happening in this sentence using "far away"?

"David and Emma live far away in the mountains."

What grammatical role do the words "far" and "away" have in that sentence?

I realize that "far away" must be an adverbial, that can be both a complement and an adjunct, when I consider the following sentences. David and Emma live far away. David and Emma are far away.

However, I'm looking for more details about the syntax within the phrase "far away". What other phrases exist with the same syntax and function? Is there a technical term here?

I'm asking in case there is something worth teaching here to my ESL students.

Solution 1:

Using the framework of the Cambridge Grammar of the English Language, far away is a preposition phrase functioning as complement of live. The head of the PP is far, which, in turn, takes a PP complment, which is headed by the preposition away. This chain of PP complements could be extended even further by adding PP from home.