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Stitz-Zeager_College_Algebra_e-book

There is no real number that comes immediately before

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Unformatted text preview: x is used. Plotting several friendly representative points should convince you that HLS1 describes the horizontal line segment from the point (−2, 3) up to and including the point (4, 3). y y 4 3 3 2 2 1 −4 −3 −2 −1 4 1 1 2 The graph of A 3 4 x −4 −3 −2 −1 1 2 3 4 x The graph of HLS1 3. HLS2 is hauntingly similar to HLS1 . In fact, the only diﬀerence between the two is that instead of ‘−2 ≤ x ≤ 4’ we have ‘−2 ≤ x < 4’. This means that we still get a horizontal line segment which includes (−2, 3) and extends to (4, 3), but does not include (4, 3) because of the strict inequality x < 4. How do we denote this on our graph? It is a common mistake to make the graph start at (−2, 3) end at (3, 3) as pictured below on the left. The problem with this graph is that we are forgetting about the points like (3.1, 3), (3.5, 3), (3.9, 3), (3.99, 3), and so forth. There is no real number that comes ‘immediately before’ 4, and so to describe the set of points we want, we draw the horizontal line segment starting at (−2, 3) and draw an ‘open circle’ at (4, 3) as depicted below on the right. 16 Relations an...
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