# Daily Desmos #253a (Advanced)

## Creator

Matt Enlow (@CmonMattTHINK)

## Difficulty

Advanced

## On to the Challenge!

Can you create the following graph using desmos.com or some other graphing tool? I’ve included the graph of #253b in blue for reference. If you’re victorious, leave a note in the comments when you’re done.

Graph looks fishily like arctan(x), but with a slope of 2 at origin and asymptotes at 10 and -10. So tried out 2/pi*10*arctan(pi*x/10) https://www.desmos.com/calculator/grne0r4r58 but still doesn’t look quiet right. Maybe a partial expansion from its Taylor series?

No Taylor expansions necessary! Check this out for a hint: http://en.wikipedia.org/wiki/Sigmoid_function

Thanks for the helpful hint! Here is my revised attempt. https://www.desmos.com/calculator/9ssgxhm83q

Well done!

Matt, I could add the blue lines as 3 separate functions, but how do you put them into 1 function?

https://www.desmos.com/calculator/t4k6id6jzr

Check out some of the functions in “functions” > “misc”…