De Anza College Vertical and Horizontal Asymptotes Questions

Write your own curve sketching problem. This will be similar to Project 2, but the function you choose does not have to be so complicated. In fact, it does not even have to be a rational function unless that is what you choose. Once you have chosen your function, answer the following.

1. Clearly state the function.
2. Find any holes or vertical asymptotes, or state if there are none.
3. Find the end behavior limx??f(x)$\underset{x??}{lim}f\left(x\right)$ and limx???f(x)$\underset{x???}{lim}f\left(x\right)$. Find any horizontal or slant asymptote, or state if there is none.
4. Find the derivative.
5. Find the intervals where the function is increasing and decreasing
6. Find all extreme values (local and global) or state if there are none.
7. Sketch a graph of the function by hand and label any asymptotes or critical points that exist.