Question

Which function does not have a vertical asymptote?

Answer 1

Which fraction has denominator that only can be equal to 0 if x is complex number?

In other word, which cannot have denominator equal to 0 in real number?

Answer 2

While you're looking at the denominators, here's another hint: x^2 is always non-negative, because if you square a real number you cannot get a negative result. (If the number you're squaring is positive, then the squaring gives positive*positive = positive, whereas if the number is negative, negative*negative = positive, and 0^2 = 0).

A rational function is undefined where its denominator is 0, so setting those denominators equal to 0, you can use the fact that

x^2 is greater than or equal to 0, so cannot be (-)

to figure out which of the options can never have a denominator of 0.