Answer
$f(x)=\frac{(x+1)(x-3)}{(x-1)^2}$
Work Step by Step
Step 1. From the given conditions, we have: $f(-1)=f(3)=0$, $f(0)=-3$, V.A. $x=1$, H.A. $y=1$,
Step 2. Thus, a possible rational function can be written as $f(x)=\frac{(x+1)(x-3)}{(x-1)^2}$