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Section 3.6
Rational Functions
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Example:
Graph
Solution:
Find the vertical asymptotes by setting the denominator equal to 0 and solving for x:
Factor.
Set each term equal to 0.
Solve for x.
Since neither of these numbers makes the numerator 0, the lines
are vertical asymptotes of the graph.
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Example:
Graph
Solution:
The horizontal asymptote can be determined by dividing both the numerator and denominator of by (the highest power of x that appears in either one).
When is very large, the fraction is very close to 0, so the denominator is very close to 1 and is very close to 2. Hence, the line is the horizontal asymptote of the graph.
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Example:
Graph
Solution:
Using this information and plotting several points in each of the three regions defined by the vertical asymptotes, we obtain the desired graph.
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13. y = 0 is the horizontal asymptote
Degree of numerator < degree of denominator
y = 0 is the horizontal asymptote

14. Degree of numerator = degree of denominator , y = 5x6 /2x6 = 5/2

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