Unformatted text preview: (why?), as soon as we found (0, 0) as the xintercept,
we knew this was also the y intercept. 2.2 Absolute Value Functions 129 y y 4 4 3 3 2 2 1 1 −3 −2 −1 1 2 3 −3 −2 −1 x f (x) = x, x < 0 1 2 3 x f (x) = x, x ≥ 0 Notice we have an ‘open circle’ at (0, 0) in the graph when x < 0. As we have seen before,
this is due to the fact the points on y = −x approach (0, 0) as the xvalues approach 0. Since
x is required to be strictly less than zero on this stretch, however, the open circle is drawn.
However, notice that when x ≥ 0, we get to ﬁll in the point at (0, 0), which eﬀectively ‘plugs’
the hole indicated by the open circle. Hence, we get
y
4
3
2
1 −3 −2 −1 1 2 3 x f (x) = x By projecting the graph to the xaxis, we see that the domain is (−∞, ∞). Projecting to
the y axis gives us the range [0, ∞). The function is increasing on [0, ∞) and decreasing on
(−∞, 0]. The relative minimum value of f is the same as the absolute minimum, namely 0
which occurs at (0, 0). There is no relative maximum value of f . There is also no absolute
maximum value...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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