Re: The relationship between types pf phonetics and its functions.
I don't know where you got the idea that phonetics has three functions. The description of how sounds are produced is what articulatory phonetics is partly about. In order to be able to discuss the sounds, some form of phonetic alphabet is required; transcription is merely denoting in print the sounds produced. It is largely a tool of articulatory phonetics.
Classification is not a function of phonetics. The labelling of certain types of sounds as vowels, semi-vowels, diphthongs, consonants, continuants, etc helps us to consider types of sounds sharing certain characteristics.
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