Hoping for a few scraps of food, the tiny puppy scooted closer to the table where the man was eating. She placed her paws on the edge of the man's seat to signal that she was hungry. The man gently eased the whining puppy back onto the floor. "No begging," he scolded. Pushing his plate away from the edge of the table, the puppy walked away from the man.

What is the function of the phrase "hoping for a few scraps of food” in the first sentence?

It is a participial phrase that modifies “puppy.”
It is an infinitive phrase that modifies “puppy.”
It is a participial phrase that modifies “man.”
It is a gerund phrase that is the subject of the sentence.