e.g. Do you often watch television?
Often is an adverb of frequency. You should put the frequency verb before an ordinary verb, after the verb be and the auxiliary.
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Is my explanation about the use of 'often' grammatical? Would you let me know whether there are any errors?
Do I have to use a frequency adverb or an adverb of frequency?
Your explanation is good. And the phrase "frequency adverb" is fine; the phrasing "adverb of frequency" is correct also, but a bit stuffy!
=)
Your explanation about the use of "often" is grammatically correct. You have correctly identified "often" as an adverb of frequency. However, there is a minor error in your statement: it should be "You should put the frequency adverb before an ordinary verb, after the verb 'be,' and after the auxiliary."
Regarding your second question, "frequency adverb" and "adverb of frequency" are essentially interchangeable terms. Both phrases refer to adverbs that indicate how often an action or event occurs. So, you can use either "frequency adverb" or "adverb of frequency" to describe words like "often," "rarely," "sometimes," etc.