A sentence can be fragmentary, but it shouldn’t be a fragment. What’s the difference?
Writers should distinguish between fragmentary sentences and sentence fragments. The following sentences are fragmentary: “A virtuoso performance? Some virtuoso.” Despite the absence of a subject and a verb, which are considered standard components of a sentence, the reader fills in the missing parts: (“[Do you call that] a virtuoso performance? [That musician is] some virtuoso.”)
A sentence fragment, by contrast, is usually a dependent clause formatted as if it were a complete sentence, such as the second sentence in the following passage: “I went to the store. Because I need to buy some toiletries for my trip.”
The form shown in the second sentence isn’t necessarily always wrong; it’s appropriate as a response in colloquial dialogue:
“Why did you go to the store?”
“Because I need to buy some toiletries for my trip.”
Otherwise, however, it’s erroneous.
It’s possible, too, for a complete sentence to be misconstrued as a sentence fragment because of a simple error such as omission of punctuation. For example, “Before I was inclined to agree” is a sentence fragment, because the words do not constitute a complete thought; no useful information has been conveyed. The implication is that a condition will be described: “Before I was inclined to agree, I needed more proof.”
If, however, before is supplied as an adverbial tag, followed by a comma (“Before, I was inclined to agree”), the wording becomes a coherent statement indicating that in the past, the writer would likely have agreed with something. Presumably, a sentence will follow with a similarly constructed reversal written in the present tense (“Now, I’m not so sure”).
However, fragmentary sentences are valid. Besides the commentary form, shown above in the examples about the alleged virtuoso, they may take the form of interjections (“Whew!” “How sad!” “What a nightmare!”), expressions (“Good job!” “So long!”), and partial imperatives (“To the castle!”) Though, of course, exclamation points are not required in fragmentary sentences, they are common, and note that such sentences are considered colloquial and should be used with caution in formal writing. You with me?