I want to draw the following function $$f(x) = \frac {1}{(\tan x)^2}$$
My intuition tells me that it does not have any x-intercepts because the numerator will never equal to zero but the online grapher shows me otherwise.
Should I put open dots or closed dots around the x-intercepts?
The function is never actually equal to $0$, but it does however tend to $0$ whenever $x$ tends to some multiple of $\frac{\pi}{2}$. This is because $tan(x)$ is not defined for $x=\frac{n\pi}{2}$ (where $n$ is a whole number). So the function doesn't actually intercept the x-axis, it just gets infinitely close to it. This means If you have to draw the function, put open dots on the x-intercepts.