The noun phrase can function as the subject or object in a sentence. The function of the noun phrase the "last slice of pizza" in this sentence is;
Noun phrases contain a noun and its modifiers. The direct object typically receives the action of the verb in the sentence.
In the sentence provided, the action, 'gave', was performed on the object, which is the last slice of pizza.
The noun phrase thus receives the action. The noun phrase can also function as the subject in a sentence.
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