Which graph represents the function? f(x)=1/x+1 +2

The parent function  is    1  / x

The parent function is shifted one unit to the left and up 2 units   by this function

In the bottom group of four  .....the correct graph is the one at the top left 

The vertical asymptote is a x = -1

And when x  = 0.....then y  = 3

Here's the graph : https://www.desmos.com/calculator/je1q765twg

Set X=0 and see where the curve crosses the Y axis.