Math Comic: Functions Behaving Badly

Published by MrHonner on

Math Comic -- Functions Behaving Badly

Categories: Appreciation


Laura Sosnowski · February 19, 2014 at 7:20 pm

I look forward to your math pictures! Thank you for them. Please tell me where I am going wrong here, about the badly behaved functions. I think the sketch is about a variety of inputs all giving the same output, right? So that is a horizontal line, and this is a perfectly fine function. Why is it behaving badly?

    MrHonner · February 20, 2014 at 9:32 am

    Hi Laura-

    You are right, this is a legitimate function. The joke is that the best-behaved functions are one-to-one. Behaving in this many-to-one manner makes certain aspects of the function difficult to deal with.

    And I’m glad to hear you enjoy the photos! Thanks for letting me know.

Andy Huynh · February 21, 2014 at 2:10 pm

It’s better to have functions that are one-to-one and onto so that there can be an inverse function. One-to-one is a better property because if a function is not onto, you can force it to be onto by restricting the codomain to its range. Now sometimes that’s easier said than done because sometimes you don’t know a function’s explicit range.

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