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If an asymptote is neither horizontal nor
vertical it is called oblique.
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Theorem Locating Vertical Asymptotes
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Vertical asymptotes x -1 and x 1
No vertical asymptotes
Vertical asymptote x -4
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1. If n lt m, then y 0 is a horizontal
asymptote of the graph of R.
2. If n m, then y an / bm is a horizontal
asymptote of the graph of R.
3. If n m 1, then y ax b is an oblique
asymptote of the graph of R. Found using long
division.
4. If n gt m 1, the graph of R has neither a
horizontal nor oblique asymptote. End behavior
found using long division.
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Horizontal asymptote y 0
Horizontal asymptote y 2/3
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Oblique asymptote y x 6