Why don't people like her?(verb) Often students like you because of your cheer.(verb) Students like you often have nervous energy.(preposition)
The first two are linking verbs, which link the subject (people, students) with its complement (her, you). The third like does not have any property of
In the last sentence, "like" is a preposition, not in the first two ones, where it is a verb.
"Like" is a preposition when we say that something looks/smells/feels like something else. For instance, "He looks like Father the Frost", which means that he is not actually Father the Frost, but reminds us of it. In the first two sentences, "like" is a verb; that is, it "does" something, it