Expert: Abe Mantell - 8/9/2006

Question
What are the four times when a function is not continuous?

I think one might be when there are vertical azmyptotes. Is that right? What are the others?

Answer
Let's see...
1. vertical asymptotes (caused by a "divsion by zero"
2. when there is an indeterminate form, for example:
-- sin(x)/x at x=0...cos(x)/(1-x) at x=0...etc.
3. when we have the even root (like square root, or 4th root)
-- e.g. the square-root(x) or the 4th-root(x)...etc.
4. piecewise defined functions.  For example:
-- f(x) = x for x<1, 2 for x>=1

OK?

Abe