Once I tried to explain what a phrasal verb is by utilizing a similar example in Portuguese. Unfortunately, I couldn't think of any example, which makes me think: are there phrasal verbs in Portuguese?
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English phrasal verbs are combinations of verbs and prepositions where the meaning of the expressions as a whole cannot be completely understood just from the meaning of the individual parts. Syntactically, there are only minor differences between phrasal verbs and actual combinations of verbs and prepositions, it's more of a semantic concept, with a lot of gray area between the two fields (see for instance Dixon, The grammar of English phrasal verbs, 1982 [subscription required]).
So if the question is whether there are verbs that, combined with a preposition, take a different meaning, the answer is yes. Just look at special entries in dictionaries under a verb. For instance, with estar (Aulete):
However, the preposition cannot stand alone, it always introduces a prepositional phrase. This would be analogous to prepositional phrasal verbs, as Wikipedia puts it (citing The Collins Cobuild English Grammar). But nothing like the particle phrasal verbs or particle-prepositional phrasal verbs, at least admitting that the particle (which then has an adverbial role) has to function also as a preposition. If we relax this requirement, then we can think of expressions such as dar-se bem (com qualquer coisa). If you deem do well (for oneself) a phrasal verb, this would probably also qualify as such.
There are also prefixes that can be added to verbs that can also work as prepositions, like sob (sobpor). However, 1) this would not analogous to phrasal verbs, more like to verbs such as understand (under + stand), 2) at least with sobpor the meaning can be deduced from the parts and 3) the are very few prefixes that also have a preposition counterpart, unlike say Dutch, where most (simple) prepositions can also function as a prefix for a separable verb (except a few like via and tijdens and some others that take a different form like met / mee).
After some research, I've found an example at Wikipedia:
"Cai fora" is analogous to "Get out", and both seems to be great examples of phrasal verbs.
This is really interesting! All Portuguese examples given by the answers here are slangs or informal/casual, being mostly used in spoken language. And it also seems that the use of English phrasal verbs has a slight difference in formality when compared to its one-word counterparts, which indeed makes much sense.
Although I can't give you any references, I dare say there aren't any phrasal verbs in Portuguese. That has been widely cited as one of the several differences between English and Portuguese. We do have, however, slang phrases that might sound like a phrasal verb: e.g. "entrar bem", where "entrar" means "enter", "go in", and "bem" means "well". Together, they mean "entrou pelo cano", "não se deu bem"
"Ele tentou enganar o professor mas no final entrou bem".