Do asymptotes always converge to a value?

1 Answer
Mar 25, 2017

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]}