How can you tell what kind of infinitive is:

-a noun
-an adjective
-or a verb?

Infinitives are verb forms. They can act in the place of nouns sometimes, but they are primarily verbs.

to go
to walk
to be
to think
to be able
to judge
to write
to read
to understand
etc.

The infinitive can also act as adjectives, example. the ability to run fast, "to run" describes what ability.

It can also be an adverb. The boy swam the river to save the dog. "to save" tells why he swam.

Check this site.
http://owl.english.purdue.edu/owl/resource/627/03/
http://www.chompchomp.com/terms/infinitive.htm

To determine the type of infinitive (whether it functions as a noun, adjective, or verb), it is important to consider its usage and role in a sentence. Here is an explanation of how to identify each type:

1. Infinitive as a Noun:
An infinitive can function as a noun when it acts as the subject, object, or complement in a sentence. To identify an infinitive as a noun, look for its position and how it interacts with other sentence elements.

Example as Subject: "To swim is my favorite hobby." (The infinitive phrase "to swim" acts as the subject of the sentence.)

Example as Object: "She loves to dance." (The infinitive phrase "to dance" acts as the direct object of the verb "loves.")

Example as Complement: "Her dream is to become a doctor." (The infinitive phrase "to become a doctor" functions as the complement of the verb "is.")

2. Infinitive as an Adjective:
An infinitive can act as an adjective to describe or modify a noun. To identify an infinitive as an adjective, observe which noun it modifies and the relationship between them.

Example: "I bought a book to read." (The infinitive phrase "to read" describes the type of book being bought.)

3. Infinitive as a Verb:
The default and most common function of an infinitive is as a verb, expressing an action or state of being. Identifying an infinitive as a verb can be based on its position in a sentence, its connection to a subject, and its ability to take direct objects or adverbs.

Example: "He wanted to eat dinner." (The infinitive phrase "to eat dinner" acts as the object of the verb "wanted." The subject "he" is connected to the infinitive.)

In summary, to determine the type of infinitive, analyze its role in the sentence: as a noun (subject, object, or complement), an adjective (modifying a noun), or a verb (expressing an action).