I need a basic math formula with the following properties:(adsbygoogle = window.adsbygoogle || []).push({});

* limit y between -1 and 3.

* (x, y) hits (-1, 0), (0, 1) and (1, 2).

* Each y value occurs only once.

I managed to do this withy=4/pi*ArcTan(x)+1. But I'd like to do this without trig. I got close withy=x*2/SQRT(1+x^2)+1. But it's not right. I keep thinking it's something simple and obvious. Can you help me?

NOTE: This is not homework. I'm graphing and analyzing some proportion data in excel for myself.

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# How to mimic 4/pi*ArcTan(x)+1 without trig

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