### Spring 2005

### Graphing Rational Functions

For the following functions, find any x and y intercepts,
asymptotes, horizontal, vertical, or otherwise, find where the
function assumes positive values and where it assumes negative
values, the places where the first derivative is either 0 or does not
exists, where the function is increasing and decreasing, find the
places where the second derivative is 0 or doesn't exist, and where
the function is concave up and concave down. Find the local maxima
and minima and points of inflection, and sketch the graph,