Does any known function behaves like flipped hyperbolic-tangent in [x, inf] and as sigmoidal in [-inf, x]?

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I want to use a transfer function for my simulation which behaves like the red-curve on the right in this picture. I do this by using a flipped hyperbolic-tangent in the range (-intercept, inf] and a sigmoidal in [-inf, intercept]. (please do look at the picture)

This is nice; it looks like what I want.

However, when change the slope parameter, I have to adjust the delta (A), and the peak becomes more...non-symmetrically smooth. I understand that the functions have different curvatures (B, C) and will behave differently away from the peak. However, what I want is a smooth peak.

Is there a single continuous function that I can use?

Any help would be greatly appreciated. :-)

PS. Here's the Python-code if you wanna take a look: https://pastebin.com/xGWNyUzi