1. Assuming the underlined phrase is 'Living in Salt Lake City,' the correct answer is gerund phrase.
Even though gerunds and participles look the same (both end in -ing), there is a difference between them. Gerunds are always used as nouns (which is the case here - the entire phrase is used as the subject of the sentence) whereas participles are used either as adjectives or adverbs.
2. Assuming the underlined phrase is 'Frustrated by the woman's response,' the correct answer is as an adjective.
Adjectives are used to describe a noun in a sentence. Here, the entire phrase is used to do that - what was the border guard like? Frustrated by the woman's response. Just ask that question and you will easily find the adjective/adjectival phrase in a sentence.
