Is "change" being used as a verb in the following sentences?

I just want to make sure that these examples are correct. Is "change" being used as a verb in the following sentences?

Her hair began to change to gray.

It’s interesting to think about how people change throughout their lives.

Solution 1:

Your two examples each illustrate one of two types of English verbs forms -- finite and non-finite. The former (in your second sentence) is the verb in the predicate of the clause

[1a] how people change throughout their lives

Finite verbs carry the sense of a verb -- conveying actions, the states of things, feelings, or equivalences. Finite verbs may be inflected for tense and number. Here change is in the present tense, but it is possible to transpose your sentence to the past tense with

[1b] how people changed throughout their lives

Your first sentence has a non-finite form of the verb, namely the infinitive, which is formed by the word to plus the plain form of the verb. (The to is elided in certain cases, as in

[2] We must [to] change our lives immediately.

This is called the bare infinitive.)

Non-finite verbs are not inflected for tense. It is not grammatical to say to changed. Infinitives find usages in sentences other than as verbs in predicates. In your first sentence, the infinitive takes the place of a noun phrase as the object of the verb began. But it could act as an adverb of purpose:

[3] I came to change the furnace filter.

No matter its usage in a sentence, we still call the infinitive a verb because it acts syntactically in many ways like a verb, e.g, it can take a direct object (that would be furnace filter in [3]).

Solution 2:

"Change" in both examples is a verb. One way to tell that it is a verb rather than a noun is to construct examples where it is modified by an adverb. Verbs can be modified by adverbs, but nouns cannot:

Her hair began to change gradually to gray.  
It’s interesting to think about how people gradually change throughout their lives.  

In sentences with related meaning using the noun "change" rather than the verb, notice that you must use the adjective "gradual" instead of the adverb "gradually":

Her hair began a gradual change to gray.  
It’s interesting to think about the gradual change that people undergo throughout their lives. 

Solution 3:

In the first sentence, "change" is being used as an infinitive. An infinitive is not itself a verb. The verb is this sentence is "began" because that is the action that the subject "hair" is performing. In this case, "to change" is modifying or describing the verb "began," so it is acting as an adverb. And began is the verb in the sentence. (By the way, I would say, "Her hair began to gray".)

In the second sentence, "change" is acting like a verb because it is something that the people are doing, but it is not the main verb of the sentence. The main verb of the sentence is "is", which is part of "It's". "Change" here is part of a long prepositional phrase.

If you wanted change to be the verb in your sentence, it would have to be the action performed by the subject of the sentence. The main verb of a sentence is the word that changes if you change the sentence's tense to past, present, future, etc. (e.g. I ate hotdogs. I EAT hotdogs. EAT is the verb.)

Anyway, to use "change" as a verb:

• Her hair changed fifty shades of gray.
• People change throughout their lives.