Hello, Raoh!

It appears to have a vertical asymptote:I'm trying to get all the possible informations about a function from its graph

and i mean by informations: limits, asymptotes . . .

. . and a horizontal asymptote:

It also seems to be a hyperbola.

The hyperbola: . .has center (0,0) and appears in Quadrants 1 and 3.

The hyperbola: . .has center (0,0) and appears in Quadrants 2 and 4.

Our hyperbola has center (-1, 1) andseemsto contain: (3,0), (1,-1), (0,-3).

I would conclude that the function is: .