I have a set of data points $f(x_i)$ for some instances $x_i$, $i\leq N$. Also, I was able to fit the curve asymptotically due to prior knowledge, i.e. I was able to fit the data to functional forms $f(x\ll x_0), f(x\gg x_0)$. How can I proceed in order to connect the two regions smoothly to fit the entire data points to a curve? Are there techniques to do this given $x_i, f(x_i), f(x\ll x_0), f(x\gg x_0)$?