In the ukWaC (not pronounced you quack) it occurs 3,952 times, that is 2.5 times per million words. As this screen shot from the Sketch Engine shows, it has a strong preference for the passive - the B in the middle of the tag indicates a form of the verb to BE. In third position, the D in VBD indicates past tense and the N in VBN indicates past participle. Since past participles are only used after the auxiliaries HAVE and BE, we can expect a significant use of perfect aspect and passive voice. This is in fact the case.
In the third column we notice by, with and to, each one telling its own story:
- with + noun phrase, most of which are Noun + of + Noun. For example: She will also be tasked with the development of strategic programming ...
- with + -ing form, mostly followed by the object of the -ing verb. For example, The review team were tasked with identifying creative but practical actions to build on existing practice.
- to + infinitive, mostly preceded by BE. The most frequent verbs: investigate, search, line, assist, and develop, produce, work. The -ing forms of some of these verbs can be seen in the screen shot also. For example, The crew were tasked to search the vehicle and establish that no persons were trapped inside.
- by + the passive's agent. The data shows that the agent is never an individual, rather an organisation in authority. For example, Banks have been tasked by the Financial Services Authority to tackle fears over internet security ...
The delexical form, give ... task occurs in the BNC 1.2 per million and in ukWaC 1.1 per million. The search is give + 3 + task. It is mostly give someone the task of doing something. The adjectives between give and task in both corpora are quite similar. In both corpora we also assign tasks, a more formal verb.
Thus the modern construction, to be tasked, has assumed a special role in the domains of business, administration, politics, whereas give a task remains in use in general English.