## Math Comic: Functions Behaving Badly

1. Laura Sosnowski says:

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 says:

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.

2. Andy Huynh says:

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.