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  1. I walked up to the ATM.

  2. I looked up at the sky.

The way I see it, "up" is an adverb in both sentences. Meanwhile, "to the ATM" and "at the sky" are prepositional phrases.

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  • "Up" is always a preposition in examples like yours. The VP "walked up to the ATM" consists of three constituents: (1) the verb "walked" + (2) the preposition "up" with no complement + (3) a preposition with an NP complement. – BillJ Oct 25 '20 at 16:33
  • See this explanation from Cambridge Dictionary. Up as an adverb - She put the books up on the highest shelf. Up as a preposition - He was up a ladder painting. But don't worry if you don't understand that distinction - I don't either! – FumbleFingers Oct 25 '20 at 16:34
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'Up' is a preposition here. According to Merrian Webster definition 3, 'up' is a preposition used in similar fashion as your examples.

For the first example sentence in the question, the applicable definition is 2a - "in a direction regarded as being toward or near the upper end or part of".

For the second example sentence in the question, the applicable definition is 1a - "used as a function word to indicate motion to or toward or situation at a higher point of"

Edit based on BillJ's inputs: Therefore, the prepositional phrases in your sentences will be "to the ATM" and "at the sky".

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  • I would't go along with you. The VP "walked up to the ATM" consists of three constituents: (1) the verb "walked" + (2) the preposition "up" with no complement + (3) a preposition "to" with the NP complement "the ATM". – BillJ Oct 25 '20 at 17:02
  • What part would you not go along with? We both call it a preposition, isn't it? – Wothla Oct 26 '20 at 6:54
  • I explained the structure in my last comment. "Up to the ATM" is not a single constituent, not a PP. It's two constituents: (1) the prep "up" and (2) the PP "to the ATM". The same applies to "up at the sky". – BillJ Oct 26 '20 at 8:14

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