Vertical Asymptotes
Vertical asymptotes are asymptotes where the value of a function is undefined at a certain point a and the function goes to infinity as x approaches x. Such asymptotes often occur in two cases:
- has a logarithm: In this case, as x approaches 0, so the vertical asymptote is at the point where the inside of the logarithm is equal to 0.
- has a fraction where the denominator is and there is at least such that . However, that value is not a vertical asymptote if it makes the numerator of that fraction a 0 as well.
An example function with asymptotes (the blue one) :