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Mentallic

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In an assignment I stated that for the graph [tex]y=x^2+\frac{1}{x}[/tex] there is an asymptote of [tex]y=x^2[/tex] for x approaching [tex]\pm \infty[/tex]. However, my teacher says that she doesn't believe it to be considered an asymptote.

So was I right or wrong to make this statement?