Unformatted text preview: sing fashion to get the graph below on the right.
y x
−3
−2
−1
0
1
2
3
4 f (x) (x, f (x))
6
(−3, 6)
0
(−2, 0)
−4 (−1, −4)
−6
(0, −6)
−6
(1, −6)
−4
(2, −4)
0
(3, 0)
6
(4, 6) 7
6
5
4
3
2
1
−3 −2 −1
−1
−2
−3
−4
−5
−6 1 2 3 4 x 1.7 Graphs of Functions 65 Graphing piecewisedeﬁned functions is a bit more of a challenge. Example 1.7.2. Graph: f (x) = 4 − x2 if x < 1
x − 3, if x ≥ 1 Solution. We proceed as before: ﬁnding intercepts, testing for symmetry and then plotting
additional points as needed. To ﬁnd the xintercepts, as before, we set f (x) = 0. The twist is that
we have two formulas for f (x). For x < 1, we use the formula f (x) = 4 − x2 . Setting f (x) = 0
gives 0 = 4 − x2 , so that x = ±2. However, of these two answers, only x = −2 ﬁts in the domain
x < 1 for this piece. This means the only xintercept for the x < 1 region of the xaxis is (−2, 0).
For x ≥ 1, f (x) = x − 3. Setting f (x) = 0 gives 0 = x − 3, or x = 3. Since x = 3 satisﬁes the
inequality x ≥ 1, we get (3, 0) as another xintercept. Next...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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