Answer:
1. noun
2. adjective
3. adverb
4. adjective
5. noun
6. noun
7. adverb
8. adverb
9. adverb
10. adverb
Step-by-step explanation:
Infinitive verbs can function as nouns, adjectives, or adverbs according to the context.
When functioning as nouns, infinitives will act like nouns do. They can be the subject, the object, a complement, or an appositive in the sentence, for instance. That is what happens in sentences 1, 5, and 6, in which the infinitive functions as a complement of a verb (1 and 5) and as the object of a preposition (6).
When the infinitive functions as an adjective, it will always modify a noun. That is what we have in sentences 2 and 4, in which the infinitives are modifying, respectively, the nouns "person" and "cycle".
Finally, infinitives functioning as adverbs modify verbs, adjectives, or other adverbs. That's what we have in sentences 3, 7, 8, 9 and 10, in which the words modified are: "came", "turned", "happy", "came", and "necessary".