Answer
Horizontal asymptote:$\qquad y=-2$
(graphed at desmos.com)

Work Step by Step
$\displaystyle \lim_{x\rightarrow\infty}(\frac{3}{x}-2)=-2$
$\displaystyle \lim_{x\rightarrow-\infty}(\frac{3}{x}-2)=-2$
Horizontal asymptote:$\qquad y=-2$
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