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?
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.
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.
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?
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.
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.