The underlined phrase "by the woman's response" is used as a prepositional phrase in the sentence.
To determine how the underlined phrase is used in the sentence, we can look at the function it serves within the sentence and the word it modifies. In this case, the underlined phrase "by the woman's response" provides additional information about the subject "frustrated." It describes the cause of the frustration. Based on this analysis, we can conclude that the phrase is used as an adverb in the sentence. Adverbs often modify verbs, adjectives, or other adverbs, and in this case, it modifies the verb "frustrated" by telling why the border guard was frustrated.
