For large variable magnitude, the value of a rational function approaches the ratio of the highest-degree terms of the numerator and denominator*. Here, that is ...
x/x = 1
f(x) approaches 1 as x approaches infinity.
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* The function approaches the line or curve defined by the quotient. (The remainder is ignored in this case.) Here, f(x) = 1 + 3/(x-3), so the quotient is the constant 1.
