$\displaystyle \mathfrak{hello}$

i'm trying to get all the possible informations about a function from its graph and i mean by informations;limits,asymptotes..

i hope someone would help me extract those informations from this example :

Let : $\displaystyle f : \mathbb{R}\to \mathbb{R}\setminus \left \{ -1 \right \}$

and here's its graph :