Final answer:
The expression 'after selling her vegetables and cocoa' is a prepositional phrase that serves an adverbial function in a sentence, modifying a verb by specifying when the action takes place.
Step-by-step explanation:
The expression "after selling her vegetables and cocoa" can be analyzed in the contexts of grammar and function within a sentence.
Grammatical Name
The grammatical name for this expression is a prepositional phrase. A prepositional phrase includes a preposition (in this case, 'after') and its object, which can be a noun, pronoun, gerund, or clause that follows the preposition. Here, the object of the preposition is 'selling her vegetables and cocoa,' which is also a gerund phrase since 'selling' functions as a gerund.
Function
The function of this prepositional phrase in a sentence acts as an adverbial phrase, which means it modifies a verb, an adjective, or another adverb by answering questions like when, where, why, how, to what extent/degree, or under what conditions. In this context, it likely modifies a verb by specifying the timing of the action described by the verb.