1. ## vertical asymptotes

is $\displaystyle \frac{1}{x^2}$ a vertical asymptote? Part of the definition is that the fraction must be a rational function, which means a function that can be expressed as a ratio of two polynomials. $\displaystyle \frac{1}{x^2}$ cannot be expressed as a ratio of two polynomials as far as I can tell. So, am I correct that it is not a vertical asymptote?

What is the most efficient way to identify a vertical asymptote?

2. I don't think you understand what a vertical asymptote is ...

vertical asymptotes are vertical lines with equations of the form $\displaystyle x = k$ where k is a constant.

the line $\displaystyle x = 0$ is the vertical asymptote of the function $\displaystyle y = \frac{1}{x^2}$

go here for a lesson ...

Vertical Asymptotes

3. ## 1 is not a polynomial

Thanks, I read that and it says, "Vertical asymptotes correspond to the zeroes of the denominator of a rational function." 1 is not a polynomial, so how can the function be a vertical asypmptote? That is, I get that analytics of it, and I know zero in the demoninator is what we're looking for. But I don't see how the function is a rational function, I want to be able to identify rational functions.

4. o.k., but understand that vertical asymptotes also exist in functions that your definition would not call "rational".