Unformatted text preview: the previous step, we know only the behavior of the graph as x → ±∞. For
that reason, we provide no x-axis labels.
In this particular case, we can eschew test values, since our analysis of the behavior of f near the vertical
asymptotes and our end behavior analysis have given us the signs on each of the test intervals. In general, however,
this won’t always be the case, so for demonstration purposes, we continue with our usual construction. 4.2 Graphs of Rational Functions 251
−3 (+) 0 (−) (+) 1 −2
3 −5 −4 −3 −1 1 3 4 5 x −1
−3 A couple of notes are in order. First, the graph of y = f (x) certainly seems to possess symmetry
with respect to the origin. In fact, we can check f (−x) = −f (x) to see that f is an odd function.
In some textbooks, checking for symmetry is part of the standard procedure for graphing rational
functions; but since it happens comparatively rarely9 we’ll just point it out when we see it. Also
note that while y = 0 is the horizontal asympt...
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