Graphing function with asymptotes at y=0,1 !my picture Hi everyone. I'm searching for a formula to describe the above function piecewise. I've tried using things like translations of $1/x$ and $\sqrt{x}$. $1/x$ gives a nice asymptotic behavior, but I'm not sure how to neutralize the side of it to the left of the $x$-axis. Any advice? Thanks.

I don't think $1/x$ is what you want, since it goes asymptotically to zero, not to one (and it is negative when $x$ is negative, not positive like you want). How about a scaled version of the arctangent on the right side (which constant would you use to scale it?), $-1/x$ on the left, and linear function in between?

Another possibility for the function on the right is $x/(x+1)$.