B. Examples3. Rational Functions

Rational functions will often have vertical and/or horizontal asymptotes.

i) Example: Graph the function shown. Use parentheses around the denominator when you enter the function. There will be vertical asymptotes x=2 and x=-2, and horizontal asymptote y=0. For this example, ZoomDec gives a good window. The lines that appear are not vertical asymptotes, although they have that appearance. They are the result of the calculator trying to connect the values plotted.

Enter the function. Press for

ZoomDec.ii) Example: Graph the function shown. The graph will have vertical asymptote x=-2/5 and horizontal asymptote y=0. The ZoomDec window does not give a good picture of the graph. 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. You can use TABLE to help you find values for the new window. When you set your window, use the fact that the y-values are quite small except when they are very close to x=-2/5.

Enter the function.

Use ZoomDec.

Enter some table

values.

Set a window.

Graph the function.

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

Enter the function. Use ZoomDec.