1. The Graph of a Rational Function
Section 4.5
The Graph of a Rational Function
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3. Analyze a Rational Function p. 228
Find domain. Den ≠0.
Reduce.
Intercepts: x-int: Num=0; y-int: Plug in x=0.
Vertical Asymptotes(V.A.): den=0 (reduced)
Horizontal Asymptotes (H.A.):
N>D is none,
N<D is y=0,
N=D is y=ratio of lead coef.
Use a graphing calculator.
Label asymptotes and intercepts. Draw graph.

4. The x-intercepts are the real zeros of the numerator that are in the domain of R. x – 1 = 0 so x = 1 is the only x-intercept.
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23. x-intercepts are –2 (even multiplicity) and 5 (odd multiplicity)
Vertical asymptotes at x = –5 and x = 2.
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24. So far we have:
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