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first thing ladies and gentlemen if you have trouble with this I would highly recommend that you pay very very close attention because this process is very very important but its also the same thing over and over its redundant when were graphing the reciprocal functions again the most important thing that I asked you guys to do or I told you guys to do for these is to not graph them but to worry about the reciprocal y equals 3 cosine of 4x lets graph this then well go through our other pieces of information yes because we we should be pretty familiar with what the cosine of 4x looks like first of all we can graph the initial period all of us should know what the initial period of cosine looks like that graph goes up to 1 it goes down to negative 1 has a period of 2pi thats what the parent graph looks like okay thats why I rather graph this than try to grow and graph that okay so but before I can graph this because this is no transformations right now we have some transformations