B. Examples
4. Rational Function Examples
Rational functions will often have vertical and/or horizontal asymptotes.
i) Example 1: Graph the function . Use parentheses. There will be vertical asymptotes of x=2 and x=2 and a horizontal asymptote of y=0. For this example, ZDECM gives a good window.
Enter the function. Using ZDECM.ii) Example 2: Graph the function . The graph will have a vertical asymptote of x=2/5 and a horizontal asymptote of y=0. ZOOM4 and ZOOM6 do not give good windows. A smaller window will work, but you will still have the vertical line showing. Just remember that the line is not part of the graph. Use TABLE to find values for a new window. When you set your window use the fact that the yvalues are quite small except when very close to x=2/5.
Enter the function.


ZDECM.


Look at table values.


Set a window.


Graph.

iii) Example 3: Graph the function . This function will have a vertical asymptote of x=0 and will also have a slant asymptote.
Enter the function. Use ZDECM.