Question

What is the vertical asymptote of this function: y=x/(x^2 + 1)

Answer 1

For rational functions such as these vertical asymptotes is when the denominator goes to zero. What would make (x^2 + 1) = 0?

No real values of x will make x^2 + 1 zero. So there are no vertical asymptotes.

Answer 2

\(x^2 + 1 = 0; ~~ x^2 = -1; ~~ x = \pm i \). Only complex values of x will make the denominator zero. No real values. Therefore, no vertical asymptotes.

Answer 3

Oh okay. Thanks!! ^^