Question

If y = 3 is a horizontal asymptote of a rational function, which must be true?
A)
lim
x→ 3
f(x) = 0
B)
lim
x→ 0
f(x) = 3
C)
lim
x→ ∞
f(x) = 3
D)
lim
x→ 3
f(x) = ∞


My answer is B

Answer 1

no, that would make it seem like y(0) = 3

But that is not an asymptote. You get a horizontal asymptote when y approaches some value for very large x. Try (C)

http://www.wolframalpha.com/input/?i=plot+y%3D3+%2B+1%2Fx,+y%3D3-3%2F(x%5E2%2B1)