A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It indicates that the function does not have a defined value at x = a.

To find vertical asymptotes of a rational function, set the denominator equal to zero and solve for x. The values of x that make the denominator zero are the vertical asymptotes, provided they do not also make the numerator zero.

If both the left-hand limit and right-hand limit at a vertical asymptote are infinite, it indicates that the function approaches positive or negative infinity from both sides of the asymptote.

The directions of limits (left-hand and right-hand limits) at a vertical asymptote indicate the behavior of the function as it approaches the asymptote, helping to understand whether the function goes to positive or negative infinity.

The left-hand limit of a function at a point is the value that the function approaches as the input approaches that point from the left side.

The right-hand limit of a function at a point is the value that the function approaches as the input approaches that point from the right side.

Vertical asymptotes indicate points of discontinuity in a function where the function does not have a defined value, typically due to division by zero.