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"this function is fulfilled" is a grammatically correct sentence and can be used in written English.
It means that a particular task or purpose has been completed or achieved. Example: The main objective of the project was to increase efficiency and this function is now fulfilled thanks to the implementation of new technology.
Exact(11)
In Drosophila, the PRC2 catalytic subunit is the single protein E z), while in mammals this function is fulfilled by two proteins, Ezh1 and Ezh2.
Today this function is fulfilled by the local primate who is sometimes called patriarch (in the autocephalous churches of Constantinople [Istanbul], Alexandria, Antioch, Jerusalem, Russia, Georgia, Serbia, Romania, Bulgaria, and Ukraine), but he may also carry the title of archbishop (in Cyprus and Greece) or metropolitan (in Poland, the Czech Republic, Slovakia, and the United States).
Today this function is fulfilled by the local primate who is sometimes called patriarch (in the autocephalous churches of Constantinople [Istanbul], Alexandria, Antioch, Jerusalem, Russia, Georgia, Serbia, Romania, and Bulgaria), but he may also carry the title of archbishop (Cyprus, Greece) or metropolitan (Poland, the Czech and Slovak republics, the United States).
In the second network, this function is fulfilled by the nucleus accumbens and caudateputamen, receiving extensive input from sensory, motor and associational cortical areas; a third analogue would by a hybrid of these two networks consisting of premotor/motor cortico-basal ganglia loops.
This function is fulfilled by two ASCL/ARP factors, Ascl1b and Neurod1.
This function is fulfilled by the Large T antigen in SV40 (5).
Similar(49)
This function was fulfilled in earlier societies by burning or hanging the king, the pope or the tax collector in effigy.
This function was fulfilled, ad hoc, by the financier J. P. Morgan in the panic of 1907.
This function was fulfilled by the EQ-5D variables that predicted patients' long-term progress as the EQ-5D unites essential aspects of subjective health.
In his more optimistic moments, he envisions a circular economy in which products are designed to be useful even after their primary function is fulfilled.
The cognitive function is fulfilled characteristically by 3rd-person nonmodal utterances (i.e., utterances in the indicative mood, making no use of modal verbs); the expressive function by 1st-person utterances in the subjunctive or optative mood; and the conative function by 2nd-person utterances in the imperative.
More suggestions(15)
this function is implemented
this function is approximated
this function is spread
this function is used
this task is fulfilled
this function is described
this function is given
this function is related
this function is represented
this rule is fulfilled
this function is approached
this vision is fulfilled
this function is defined
this assumption is fulfilled
this criterion is fulfilled
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com