Final answer:
The sentence 'They've been playing good jazz for years.' is a complete sentence as it contains a subject and a predicate, expressing a full thought. Sentence fragments lack this completion and should be used carefully.
Step-by-step explanation:
The sentence 'They've been playing good jazz for years.' is a complete sentence because it has both a subject ('They') and a predicate ('have been playing good jazz'), and it expresses a complete thought. On the other hand, a sentence fragment lacks at least one of these components and does not form a complete thought. To avoid sentence fragments, one must make sure that every sentence has a subject, a verb, and expresses a complete thought. Sometimes, fragments can be used intentionally for stylistic purposes in creative writing or advertising, but they should be avoided in formal academic writing unless their use is purposeful and clear.