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I asked a question about parallel functions in here . I understood that offset curves that are the parallels of a function may not be functions after J.M.'s answer. I got new questions after that answer.

Q1) What is the limit distance to the base function if offset curve is a function too?

Q2) It can be shown as geometrically that all parallel curves of line and half circle are also functions. What is the whole function family defination for such functions?

Thanks for answers

Please see parallel curve examples below. (Thanks to J.M. for the graphs) enter image description here

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