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I want to describe function that is monotonic increasing/decreasing up to some point, and then is allowed to switch to be monotonic decreasing/increasing (the other direction). In other words, it "goes up then down" or "goes down then up", but switches direction at most once. The best description I can think of is "double monotonic", but is there an official term for this?

Note that just like the regular "monotonic", this doesn't make any assumptions about the domain (continuous or discrete, finite or infinite, etc).

aiai
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    The term "bitonic" is in use in at least one context. –  Sep 17 '15 at 07:55
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    Such a function is called unimodal, see here: https://en.wikipedia.org/wiki/Unimodality#Unimodal_function – Christian Blatter Sep 17 '15 at 07:55
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    These are both nice terms. Thanks. (The definition of "unimodal" seems to match a little better than the definition of "bitonic", especially since "bitonic" has this weird extra part "or a circular shift of such a sequence". On the other hand, I like how the word "bitonic" is evolved from "monotonic", instead of "unimodal" which evolved from "mode" in statistics.) – aiai Sep 17 '15 at 08:29

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