1. Rational Functions Objectives: Graph rational functions.
Determine vertical, horizontal, and slant asymptotes.
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5. y y = R(x) y = L x y y = L x y = R(x) JReasons
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7. x = c y x
x = c y x
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8. If an asymptote is neither horizontal nor vertical it is called oblique (slant).x
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11. Theorem Locating Vertical Asymptotes
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13. Vertical asymptotes: x = -1 and x = 1
No vertical asymptotes
Vertical asymptote: x = -4
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14. 1. If n < 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 > m + 1, the graph of R has neither a horizontal nor oblique asymptote.
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16. Horizontal asymptote: y = 0
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17. Oblique asymptote: y = x + 6
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