Question

Do asymptotes always converge to a value?

Answer 1

No. The function is undefined at the asymptote value.

Explanation:

Asymptotes go from `(-oo, oo)`

When a function has a vertical asymptote at a `x-value` the function never reaches that value.

Ex. `y = 1/(x-5)`

The vertical asymptote is at `x = 5` At `x = 5` the function is undefined. See the graph below:

graph{1/(x-5) [-5.41, 14.59, -6.04, 3.96]}