What are the horizontal and vertical asymptotes of r (x) = (6x+1) / (16x^2) + 1?

Horiz. asy.: experiment with letting x grow larger and larger (without bound). Eventually the given expression will approach some limiting value.

If we continue to increase x in (6x+1) / (16x^2), the fraction will approach 0. Try it!

If we continue to increase x in (6x+1) / (16x^2) + 1, the expression will approach 0 + 1, or 1.

Which one did you mean?

Thus, the horiz. asy. would be y=0 or y=1.

Vertical asy.: Identify the x-value, if any, at which the denominator of this fraction = 0.

If you meant (6x+1) / (16x^2) (without the + 1), the fraction is undefined at x=0. Thus, the vert. asy. is the vertical line x=0.