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f(x)= \[\frac{ x }{ x^2 +1 }\]

solve
x^2 + 1 = 0
for x

tell me what you get

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?

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?

So basically the numerator was pointless in this equation?

pretty much

Got it, thank you again.!

sure thing