Set the denominator x^2+1 equal to zero and solve for x x^2+1 = 0 x^2 = -1 x = sqrt(-1) or x = -sqrt(-1) x = i or x = -i The two results (i and -i) are nonreal values
There are no real numbers we can plug into x^2+1 to get to 0 The smallest x^2+1 can get is 1 Because its not possible to have x^2+1 be zero (if x is real) this means we don't run into dividing by zero errors. This is why there are no vertical asymptotes.
