Try these problems.

Consider Find all vertical asymptotes.
There are vertical asymptotes There are no vertical asymptotes
Consider Find all vertical asymptotes.
There are vertical asymptotes There are no vertical asymptotes
Write your answers from least to greatest:

Give intervals on which each of the following functions are continuous. Write combinations of intervals going from left to right on the number line.

(a)
is continuous on .
(b)
is continuous on and and .
(c)
is continuous on .
(d)
is continuous on .

Let Is continuous everywhere?

Yes No

Let

Find

(a)
(b)
(c)
(d)
(e)
(f)
The Intermediate Value Theorem states: If is a continuous function for all in the closed interval and is between af(a) and bf(b) , then there is a number uf(u) in such that f(u) = rf(r) = u .
Consider the following graph:

Is the function continuous at or ?

is continuous at both and . is continuous at but not at . is continuous at at but not at . is not continuous at and .

Let be continuous on where and . Does a value exist such that ?

There does not exist a value. Yes, by the Intermediate Value Theorem Yes, by the Mean Value Theorem There does not necessarily exist such a value