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, ZOOM
4 gives a good window.
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Enter the function.
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Using ZOOM4.
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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 should use dot
mode so that the vertical line is not included. 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. |
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| ZOOM4 |
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| Look at table
values. |
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| Set a window. |
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| Graph. |
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iii) Example 3:
Graph the function 
. This function will have a vertical asymptote of x=0 and will also have
a slant asymptote.
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Enter the function.
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Use ZOOM4.
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