Definition:

An idiomatic expression that combines a verb and a preposition to make a new verb with a distinct meaning.

The preposition in a prepositional verb must be followed by a noun or pronoun, and so all prepositional verbs are transitive. Also, the object must come after the preposition.

See also:

• Compound Verb
• Particle Movement
• Phrasal Verb
• Prepositional Adverb
• Ten Quick Questions and Answers About Verbs and Verbals

Examples and Observations:

• "God has cared for these trees, saved them from drought, disease, avalanches, and a thousand tempests and floods. But he cannot save them from fools."
  (John Muir)
• "The difference between the old ballplayer and the new ballplayer is the jersey. The old ballplayer cared about the name on the front. The new ballplayer cares about the name on the back."
  (Steve Garvey)
• "I believe in equality for everyone, except reporters and photographers."
  (Mahatma Gandhi)
• "A prepositional verb consists of a verb plus a particle which is clearly a preposition: for example, look at, send for, rely on. These are mostly lexically singly stressed, with a primary stress going on the verb. Thus look at has the same stress pattern as edit or borrow. The second element, the preposition, being unstressed, does not get accented (unless for contrastive focus)."
  (John Christopher Wells, English Intonation. Cambridge Univ. Press, 2006)
• Prepositional verbs consist of a transitive verb plus a preposition with which it is closely associated.
  
  • He stared at the girl.
  • She finally decided on the blue car.
  Prepositional verbs do not take the particle movement rule. The verb and the following preposition can be separated by an adverb, and the preposition can precede a relative pronoun and appear at the beginning of a wh- question.
  • He stared intently at the girl.
  • The girl at whom he was staring was strikingly beautiful.
  • At whom was he staring?
  (Ron Cowan, The Teacher's Grammar of English. Cambridge Univ. Press, 2008)

• The Difference Between Phrasal Verbs and Prepositional Verbs
  "There are a number of syntactic criteria you can use for distinguishing phrasal verbs from prepositional verbs:
  1. in transitive phrasal verbs, the particle is movable, but the preposition in a prepositional verb is not;
  2. the NP is the object of the verb in phrasal verbs rather than of the preposition;
  3. in both transitive and intransitive phrasal verbs, the particle carries stress, as in She took the cap off or The plane took off, while prepositions are unstressed, as in We knocked on the door.
  4. adverbials cannot intervene between the verb and the particle whereas they can between the verb and the preposition, *looked quickly up the information, but looked quickly into the oven.
  (Laurel J. Brinton, The Structure of Modern English: A Linguistic Introduction. John Benjamins, 2000)