If y = 3 is a horizontal asymptote of a rational function, which must be true?

Question

lim
x→ 3
f(x) = 0 <<my answer

lim
x→ 0
f(x) = 3

lim
x→ ∞
f(x) = 3

lim
x→ 3
f(x) = ∞

Answer 1

Surely you don't want help from someone who doesn't know this subject!!

Answer 2

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Answer 3

3 as an asymptote means that is the value that the function approaches as x goes to infinity