What part of speech is the infinitive phrase used? Is this a noun, adjective, or adverb?

1. The coach's example is one to take seriously.

2. We all made an effort to work harder.

3. The contest requires all entries to be mailed by Thursday.

4. The players were eager to try on their new uniforms/

5. The director asked Mindy to audition for the part

6. The children did not want to wait till dinnertime.

7. The innkeeper provided us with a place to spend the night.

8. This is the best place to find that game.

9. All of us will have to sell some of these tickets.

10. Vera's parents encouraged her to apply for the job.

I'm sorry but I looked up the ways to tell the difference but I still don't know how.

http://grammar.ccc.commnet.edu/grammar/phrases.htm#infinitive

Take a look at the first section here in which infinitive phrases are explained and illustrated.

All of the infinitive phrases in these sentences occur AFTER the main verb in each sentence, right? Some are immediately after the verb; those are either nouns (serving as direct objects or predicate nouns) or possibly as an adverb.

Others are after a noun or pronoun that occurs after the main verb. Those will be either nouns (serving as appositives) or adjectives (if they modify/describe the noun immediately before it).

1. The coach's example is one to take seriously.
This seems like a noun, acting like an appositive.

Think about the others and let me know what you decide.

Consider

... OR do you think the infinitive here is an adjective, modifying/describing "one"?

The coach's example is one to take seriously.

answers please

I want to know the rest answer.

we all made an effort to work harder

The contest requires all entries to be mailed by Thursday

Determining the part of speech of an infinitive phrase can be tricky, as it depends on how it is used in a sentence. An infinitive phrase typically contains an infinitive verb, which is the base form of a verb preceded by the word "to." In most cases, the function of an infinitive phrase is determined by its role in the sentence.

To help with determining the part of speech, here is an explanation for each sentence:

1. The coach's example is one to take seriously.
- The infinitive phrase "to take seriously" serves as an adjective modifying the noun "one." It answers the question "which one?"

2. We all made an effort to work harder.
- The infinitive phrase "to work harder" functions as an adverb modifying the verb "made." It answers the question "how?"

3. The contest requires all entries to be mailed by Thursday.
- The infinitive phrase "to be mailed" serves as an adjective modifying the noun "entries." It answers the question "what kind of entries?"

4. The players were eager to try on their new uniforms.
- The infinitive phrase "to try on their new uniforms" acts as an adverb modifying the adjective "eager." It answers the question "why were they eager?"

5. The director asked Mindy to audition for the part.
- The infinitive phrase "to audition for the part" serves as a noun, functioning as the direct object of the verb "asked." It answers the question "what did the director ask Mindy?"

6. The children did not want to wait till dinnertime.
- The infinitive phrase "to wait till dinnertime" functions as a noun, serving as the direct object of the verb "want." It answers the question "what did the children not want?"

7. The innkeeper provided us with a place to spend the night.
- The infinitive phrase "to spend the night" functions as a noun, serving as the object of the preposition "with." It answers the question "what did the innkeeper provide us with?"

8. This is the best place to find that game.
- The infinitive phrase "to find that game" acts as an adjective modifying the noun "place." It answers the question "which place?"

9. All of us will have to sell some of these tickets.
- The infinitive phrase "to sell some of these tickets" functions as an adverb modifying the verb phrase "will have to sell." It answers the question "why will all of us have to?"

10. Vera's parents encouraged her to apply for the job.
- The infinitive phrase "to apply for the job" serves as a noun, functioning as the direct object of the verb "encouraged." It answers the question "what did Vera's parents encourage her to do?"

By analyzing the role of the infinitive phrases in each sentence and considering the questions they answer, you can determine their part of speech.