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This is a single word adjective that is in general use, but which has a specific use as a semi-technical term in mathematics.

It's something like a "pessimistic" function, or a "lethal" function?

It has the connotations of a function that only exists in order to prove that an edge case could in principle exist. A function that has been deliberately designed to try to break something.

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    This would be better on Maths.SE, but do you mean 'pathological'?
    – Edwin Ashworth
    Sep 24, 2017 at 13:58

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The word is 'pathological', as suggested by @Edwin.

This is a specific application of it's general language meaning: being such to a degree that is extreme, excessive, or markedly abnormal https://www.merriam-webster.com/dictionary/pathological (#3)

In mathematics the connotations are Having properties which are counterintuitive or difficult to handle. https://en.wiktionary.org/wiki/pathological (#3)

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    I think the full OED's second cite for this usage (1946, the first being 1939) is interesting: We can speak of a function of x that is equal to 1 if x is rational but to 0 if x is irrational. Such a function would be fairly regarded by a physicist as pathological, and he is interested in a much narrower class of functions, roughly speaking such as can be represented by graphs. A program running that function on all numbers (both rational and irrational) from 0 up would never get past the infinitely small to reach the first rational number greater than zero (an "infinitely rare" case).
    – FumbleFingers
    Sep 24, 2017 at 16:09

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