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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.
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.
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Enter the function.
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ZDECM.
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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.
