I'm looking for a shirt for my dad.

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Does 'for my dad' modify 'shirt' or 'looking'?

Is 'for my dad' an adjective phrase or an adverbial phrase?

2 answers

It modifies shirt, so is an adjective phrase.
The other fellow here is mistaken. If you were looking for your dad (who was missing), it would be adverbial, modifying "looking." In this case, it modifies shirt.