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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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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