Question

Let f(x)=20/(1+9)^(e3x)

Answer 1

There's an error in your version of the function.  Compare yours to the original post.

Consider what happens to this function as x becomes increasingly large:
the denominator grows quickly and without bound.  The numerator stays the same.  In such a situation, the function goes to zero as x increases.  Thus, y = 0 is the horiz. asympt.  The denom. is never zero, so there are no vert. asymp.