Unformatted text preview: f the functions g , h, and i in Example 2.2.1 starting
with the graph of f (x) = x and applying transformations as in Section 1.8. For example, the for
the function g , we have g (x) = x − 3 = f (x − 3). Theorem 1.3 tells us this causes the graph of f
to be shifted to the right 3 units. Choosing three representative points on the graph of f , (−1, 1),
(0, 0) and (1, 1), we can graph g as follows.
y y 4 −3 −2 −1 3 2 (−1, 1) 4 3 2 (1, 1) 1 (0, 0) 1 2 f (x) = x 1 3 4 5 x shift right 3 unit −− − − − −→
−−−−−−
add 3 to each xcoordinate −3 −2 −1 (2, 1)
1 (4, 1)
2 (3, 0) 4 5 x g (x) = f (x − 3) = x − 3 Similarly, the graph of h in Example 2.2.1 can be understood via Theorem 1.2 as a vertical shift
down 3 units. The function i can be graphed using Theorem 1.7 by ﬁnding the ﬁnal destinations
of the three points (−1, 1), (0, 0) and (1, 1) and connecting them in the characteristic ‘∨’ fashion.
While the methods in Section 1.8 can be used to graph an entire family of absolute value functions,
not all functions involving absolute values posses the characteristic ‘∨’ shape, as the next example...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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