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What are the asymptotes?

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1 Answer

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.

Comments

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|).