Which component of language can either be a whole word or a part of a word?

The correct answer is morpheme. A morpheme is the smallest meaningful unit of language that can stand alone as a word or can be a part of a word. For instance, the word "cats" consists of two morphemes: "cat," which can stand alone as a word, and "s," which is a suffix that provides additional meaning about plurality.

This concept distinguishes morphemes from the other components listed. Graphemes refer to the smallest units of writing in a language, such as letters or characters, which do not convey meaning on their own when isolated. Phonemes are the smallest units of sound in a language that distinguish meaning but don't represent written forms directly. A gerund is a form of a verb that ends in -ing and functions as a noun; it is specific to verb forms rather than being a broad category like morphemes. Thus, morphemes are unique in their ability to serve as both whole words and parts of words, making it the correct answer to the question.