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What are the asymptotes?

What are the asymptotes of the graph of the parametric equations x=1/t, y=t/(t+1)?
Answer: x=-1, y=0.

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Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
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x=1/t; y=t/(t+1)=1/(1+1/t)=1/(1+x)
So y=1/(x+1), obviously x=-1 is an asymptote, another one is y=0, when x goes to infinity.


x=-1 is a vertical asymptote (function never crosses a vertical asymptote).
y = 0 is a horizontal asymptote, but only at large values of |x| (function may cross horizontal asymptote at small values of |x|).