The graph shown here is the graph of which of the following rational functions ?

The first thing you should do for this case is to study the domain of the function to verify the values of x for which it is defined.
 We have then the domain of the function is:
 x = (- inf, -1)
 x = (- 1, 3)
 x = (3, inf)
 Equivalently all the x that belong to:
 (-inf, -1) U (-1, 3) U (3, inf)
 Therefore, the function is:
 F (x) = (x-2) / ((x + 1) * (x-3))
 answer
 A. F (x) = (x-2) / ((x + 1) * (x-3))