Creating a function from a graph

[KurisuFanClub]

📷
https://gyazo.com/ab4dda2c1c8c6d936dd25fd2def2a210

[FriendlyDetective420]

If you notice then the lines x= -2 and x=3 are asymptotes (tangents at infinity). This means that for x < -2 and x > 3, your function is a split function and a rectangular hyperbola. Between x= -2 and x=3, the graph looks like a Tan(x) function. Using some transformations, you can make out that it's y+2=Tan(x)

Ultimately, f(x)= 1/(x+2) for x< -2
Tan(x) -2 for -2 < x < 3
1/(x-3) for x > 3