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Unformatted text preview: e graphs of rational functions. Consider the function f (x) = 2x+11
from Example 4.1.1. Using a graphing calculator, we obtain 1 You should review Sections 1.2 and 1.4 if this statement caught you oﬀ guard. 234 Rational Functions Two behaviors of the graph are worthy of further discussion. First, note that the graph appears
to ‘break’ at x = −1. We know from our last example that x = −1 is not in the domain of f
which means f (−1) is undeﬁned. When we make a table of values to study the behavior of f near
x = −1 we see that we can get ‘near’ x = −1 from two directions. We can choose values a little
less than −1, for example x = −1.1, x = −1.01, x = −1.001, and so on. These values are said to
‘approach −1 from the left.’ Similarly, the values x = −0.9, x = −0.99, x = −0.999, etc., are said
to ‘approach −1 from the right.’ If we make two tables, we ﬁnd that the numerical results conﬁrm
what we see graphically.
−1.0001 f (x)
(x, f (x))
3002 (−1.001, 30...
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