For the following functions, use "x" to indicate that the $x$-axis is an asymptote, "h" to indicate a horizontal asymptote other than the $x$ axis, "v" to indicate a vertical asymptote, "s" to indicate a slanted asymptote, and "n" the lack of an asymptote. If the graph of a function has several types of asymptotes indicate them all in alphabetical order.

$f(x) = \frac{x}{x-1}.$
$f(x) = \frac{x}{x^2-1}.$
$f(x) = \frac{x-1}{x^2+1}.$
$f(x) = \frac{x^4}{x^2+1}.$