You're confusing prepositions and "prepositional verbs".
Multi-word verbs are verbs which consist of a verb and one or two particles or prepositions (e.g. up, over, in, down). There are three
types of multi-word verbs: phrasal verbs, prepositional verbs and
phrasal-prepositional verbs. Sometimes, the name ‘phrasal verb’ is
used to refer to all three types.
For example, I've found where you have gotten your quote from and it even provides a table of "prepositional verbs". Notice how the "prepositional verb" which consists of the verb and preposition next to each other and cannot be separated:
This statement isn't exactly true such as with transitive and intransitive prepositional verbs. BUT what is true is that you cannot move the preposition anywhere you like and if you can, it is usually in a certain syntactic position such as in between a verb and its object or not at all in intransitive prepositional verbs. << Of course, where it is clear there is no prepositional verbs present this rule does not apply, it only applies to 'special' verb phrase constructions. This is the case for the OP's examples, which will be explained in more detail.
At what are you looking?
After whom are you looking?
From what did you prevent me?
Of what are you accusing me?
In these sentences, they are prepositions and the verbs are clearly separated and so are not prepositional verbs.
If this is so, what are 1-4? The prepositions in 1-4 are not “prepositional phrases”. In 1-4 there is no direct object. The verb and preposition are always separate. The preposition’s object in 1-4 is the what-phrase. 1-4 is more formal.
If we reworded the above so that the preposition shifts to the clause-final position, it would make the below questions more casual and “informal” according to register.
What are you looking at?
Whom are you looking after?
What did you prevent me from?
What are you accusing me of?
5-8 are not prepositional verbs, though they can be. There are two types of prepositional verbs: transitive and intransitive. For example, we know in 5 to 8 are just ordinary prepositions because they can be reworded as in 1-4 and still maintain the same meaning. 5 and 6 may look like a prepositional verb, we know it is not because it has a direct meaning compared to other prepositional verbs, and also because of 1 and 2...its function is not the same as normal prepositional verbs even though one can argue syntactically that it is a prepositional verb; in the examples above "looking at" and "looking after" has an easy deducible meaning and so not a prepositional verb, as prepositional verbs have a special meaning, often idiomatic. There are contexts where "look after" and "look at" can be interpreted as transitive-prepositional verbs.
When is “look at” and “look after” a prepositional verb? This will be discussed below. To make it easier think of prepositional verbs as phrases, and prepositions as a separate single unit. If they can be separated then it likely they are not prepositional verbs. There are exceptions to this. Prepositional verbs can be transitive and intransitive. Transitive-prepositional verbs can be separated.
Prepositions vs preposition verbs:
Usually, transitive-prepositional verbs don’t make sense without an object:
He looked at her.
In the above sentence, there are certain tests to determine whether it is a prepositional verb by seeing if the preposition at and the verb can be separated and still maintain the same meaning:
✗ *He at her looked
Why is the above wrong? There is a certain rule with pronouns discussed later.
and we know it is a transitive-prepositional verb because if we removed the direct object the sentence wouldn’t make sense:
✗ He looked at _____ .
You can construct sentences where “look at” is not a prepositional verb such as example 5 and 6.
✗ It’s hard work looking after _______ .
Again “look after” can again be a “prepositional verb” depending on the syntatic structure of the sentence. Compare this sentence with example 6.
The preposition (or particle) cannot be moved or separated in intransitive-prepositional verbs:
✓ We broke up two years ago
✗ We broke two years ago up
With transitive-prepositional verbs it is different:
If the direct object is a noun, you can say:
✓ They pulled down [the house]
✓ They pulled [the house] down
If the object is a pronoun (such as it, him, her, them) , then the object always comes between the verb and the particle (adverb/preposition etc.):
✓ They pulled [it] down.
✗ They pulled down [it].
If there is a clear direct object and there is a pronoun, then the preposition must always come between the verb and the direct object:
✓ He looked at her.
✗ At her he looked.
✓ It’s hard work looking after three children all day.
✗ Looking after three children all day it's hard work
✓ Looking after three children all day is hard work
We know 1-4 aren't 'prepositional verbs', not only because of the reasons cited earlier, but because the meaning is direct and clear and prepositional verbs tend to have a nuanced meaning which requires a certain context or understanding, for example prepositional verbs such as break into, get over, break up etc.
To illustrate consider the difference in semantics between:
They pulled down the house.
They pulled the house down.
With the first being a transitive-prepositional verb "pulled down", but in the second it is also a transitive-prepositional verb with the object in between the verb and the particle - notice, how even though the second is more direct, we know its meaning does not stray far from that conveyed in the first. In fact we could almost interpret both sentences as almost equivalent in meaning. We should not however ignore its syntactic difference. With "pulled down" being a prepositional verb "phrase" and and in the second, the particle being separated from the verb. Remember the term 'phrase' is flexible,
brave cat can be a noun phrase and so can nouns e.g.
Mary. Mary's part of speech is always categorically a noun but can function as a noun phrase in clauses/sentences.
Prepositions vs Phrasal verbs https://www.temple.edu/writingctr/english-language-learners/documents/Prepositionsvs.Prepositionalphraseshandout.pdf
- italics are the verbs
- bold are the prepositions
- Is there a direct object?
Yes -> If the preposition and verb can be reordered to fit in between the object; then it is likely to be a transitive prepositional phrase. There are exceptions in re-ordering if the direct object is a noun or a pronoun.
No -> Go to 2
- Can they verb and preposition be separated?
Yes -> It is not a intransitive prepositional verb. If you failed the first test it is not a transitive prepositional verb either.
No -> It is likely an intransitive prepositional verb
There are further tests to see whether a phrase is a prepositional verb or not IF they are grammatically syntactically similar:
- What is the function of the phrase - literal or idiomatic?
literal - you can understand the meaning of the words on a surface level with no nuance and each word is clear as to its role or function - it is likely not a prepositional verb.
idiomatic - if 2 or more words convey an enhanced layer of meaning beyond the literal meaning of each word - it is likely to be a prepositional verb.