f(x)=(x2+1)/(x2-1); x2-1=0 when (x-1)(x+1)=0, that is, when x=1 or -1 (these are the vertical asymptotes).
f(0) is the y-intercept: 1/-1=-1; f(x)=0 would be the x-intercept, but x2+1 cannot be zero so there is no x-intercept.
The horizontal asymptote is found by replacing x with a very large number, X, so f(X)≈X2/X2=1, making the horizontal asymptote y=1.