维基百科英文版：phrasal verb 短语动词

In English, a phrasal verb is a phrase such as turn down or ran into which combines two or three words from different grammatical categories: a verb and a particle and/or a preposition together form a single semantic unit. This semantic unit cannot be understood based upon the meanings of the individual parts, but must be taken as a whole. In other words, the meaning is non-compositional and thus unpredictable.^[1] Phrasal verbs that include a preposition are known as prepositional verbs and phrasal verbs that include a particle are also known as particle verbs. Additional alternative terms for phrasal verb are compound verb, verb-adverb combination, verb-particle construction, two-part word/verb, and three-part word/verb (depending on the number of particles), and multi-word verb.^[2]

verb phrase 动词短语

In linguistics, a verb phrase (VP) is a syntactic unit composed of at least one verb and its dependents—objects, complements and other modifiers—but not always including the subject. Thus in the sentence A fat man put the money quickly in the box, the words put the money quickly in the box are a verb phrase; it consists of the verb put and its dependents, but not the subject a fat man. A verb phrase is similar to what is considered a predicate in more traditional grammars.

   副词小品词往往与动词连用，构成双词动词，有时会产生全新的意思（如 break down, put off, work out, give up）。这些词通常叫做“短语动词”（phrasal verb）。（摘自《牛津英语用法指南》第三版20.2）

你似乎对第三个案例有误解，第三个案例里边，狭义，look after ,look at都是介词动词。介词动词，和保持原义没必然联系。

A：短语动词：有动词+小品词（介词/副词）构成的动词词组。

(1)动词+介词：

look at

look after 

look for

laugh at

come across

(2)动词+副词：

take off

put on

look up

have on

take away

put aside

put away

B:动词短语：由动词+名词+介词 构成的动词词组。

take a look at

catch hold of

catch sight of 

take the place of 

take care of