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Find the vertical asymptotes, if any, of the graph of the rational function.

Mathematics
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f(x)= \[\frac{ x }{ x^2 +1 }\]
solve x^2 + 1 = 0 for x
tell me what you get

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Would it just be x^2 = -1 ?
good so far, what's next?
there will be no vertical asymptote
Hmm, Im not sure? Do I replace the variable with -1?
take the square root of both sides x = sqrt(-1) or x = -sqrt(-1) but there's a problem, you can't take the square root of -1 and get a real number
so x^2 + 1 = 0 has no real solutions
leading to the fact that \[\Large \frac{ x }{ x^2 +1 }\] has no vertical asymptotes
Ah, ok. Thank you.! Just out of curiosity, what happened to the x on top of the fraction?
the numerator doesn't play any role in finding the vertical asymptotes unless you can make it cancel with something in the denominator
if you had something like x -------- x^2+x the fraction would simplify to 1 ________ x + 1 and this would be a case where the numerator plays a role
So basically the numerator was pointless in this equation?
pretty much
the basic thing is to simplify as much as possible (which couldn't be done in this case) then look at the denominator only
Got it, thank you again.!
sure thing

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