This is the cranial nerve involved in the process of olfaction - the sense of smell.
It is not a routine part of the neurological examination to test the function of the olfactory nerve - its function is assessed subjectively by asking the patient if they can smell things, and whether their sense of smell has altered recently; many patients will notice a loss of taste first - this should trigger the same line of investigation. Note that this line of enquiry will only elicit bilateral anosmia, and that if there is any suspicion of a lesion then each nostril ought to be formally tested.
Testing can be grossly performed by pressing a nostril closed, exposing the other to cut orange peel or soap, determining whether the patient can smell this with eyes closed, and then repeating on the other side.
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