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    Is there a rule for sketching graphs? Like what to do first in terms of stretching the graph, translating the graph up and down and reflecting it? Does this order change when you have a modulus?


    Well. On the point about modulus. I would sketch without the modulus first and then reflect the graph for y<0 in the x axis.

    Your question is not very specific but in general I look for whether I recognise the function and consider x>>0 x<<0 and any singularities.

    If I recognise the function I look for f(kx) f(x+a) kf(x) f(x)+k in order to identify transformations.

    The way you go about such things is not really formulaic but depends on the question.
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