II. Setting a Window - Finding One That Works

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 y-values are quite small except when very close to x=-2/5.

Enter the function.
Look at table values.
Set a window.

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.


1. Polynomial
2. Trigonometric
3. Radical
4. Rational
5. Exponential
6. Logarithmic