If a function admits horizontal asymptote at $-oo$ but at $+ oo$ does not admit,she can admit oblique asymptote to $+ oo$ ?

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Answer 1 · 2017-05-06T20:57:20

Yes

Consider the function:

$f(x) = 1/(1+x^2)+(x+abs(x))/2$

This is continuous on the whole of $RR$ , with horizontal asymptote $y=0$ and oblique asymptote $y=x$

graph{1/(1+x^2)+(x+abs(x))/2 [-10, 10, -5, 5]}

If a function admits horizontal asymptote at -oo-oo but at + oo+ oo does not admit,she can admit oblique asymptote to + oo+ oo?