A function y = f(x) has a vertical asymptote at x = c if,
f(x) is continuous for values of x just above c and the value of f(x) becomes infinitely large or infinitely negative (but not oscillating between them) as x approaches c from above. The function could behave similarly as x approaches c from below.
In such a case f(c) is a singularity: the function is not defined at that point.
Chat with our AI personalities
It remains a vertical asymptote. Instead on going towards y = + infinity it will go towards y = - infinity and conversely.
false
Undefined
The domain of the function f(x) = (x + 2)^-1 is whatever you choose it to be, except that the point x = -2 must be excluded. If the domain comes up to, or straddles the point x = -2 then that is the equation of the vertical asymptote. However, if you choose to define the domain as x > 0 (in R), then there is no vertical asymptote.
No. For example, in real numbers, the square root of negative numbers are not defined.