The document provides information about finding vertical asymptotes of functions. It states that vertical asymptotes occur when a function is undefined, usually at the zeros of the denominator, and that the limit of the function is plus or minus infinity at these points. It also provides an example of a lame joke before discussing vertical asymptotes in more detail, including exceptions when common factors can be canceled.

1. AP Calculus Warm up
8.26.13
Find the vertical asymptotes of each function:
1
1
)(
x
xf
3
)2(
4
)(
x
xf
16
2
)( 4
2
t
tt
xf

2. The Lame Joke of the day..
What do cats eat for breakfast?
And now it’s time for..
Mice Krispies!

3. Vertical Asymptotes
• Vertical asymptotes occur when a function is
undefined (usually the zeros of the denom.)
• At a vertical asymptotes, the limit of the
function is +/- infinity ( does not exist)
• At the asymptote, the function increases or
decreases without bound.
• Also,
cxcx
limlim

4. Vertical Asymptotes - exceptions
• The exception is when you can cancel
common factors - YOU get a hole instead of
an asymptote