Good thought Raoh, but this is not the case. Look at the graph skeeter has posted.
You can think of a vertical asymptote as any value of the function of x that x is "not allowed" to be. Is there any such value?
Limits at infinty tell us about y, not x. Think about what you said. By makink the statement , you're assuming that x can be ANY NUMBER!
P.S. You were correct about the horizotal asymptote.