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**Unformatted text preview: **x > 0 To graph this function, we graph two horizontal lines: y = −1 for x < 0 and y = 1 for x > 0.
We have open circles at (0, −1) and (0, 1) (Can you explain why?) so we get
y −3 −2 −1 f (x) = 1 2 3 x |x|
x As we found earlier, the domain is (−∞, 0) ∪ (0, ∞). The range consists of just 2 y values:
{−1, 1}.2 The function f is constant on (−∞, 0) and (0, ∞). The local minimum value of f
is the absolute minimum value of f , namely −1; the local maximum and absolute maximum
values for f also coincide − they both are 1. Every point on the graph of f is simultaneously
a relative maximum and a relative minimum. (Can you see why in light of Deﬁnition 1.9?
This was explored in the exercises in Section 1.7.2.)
2. To ﬁnd the zeros of g , we set g (x) = 0. The result is |x + 2| − |x − 3| + 1 = 0. Attempting
to isolate the absolute value term is complicated by the fact that there are two terms with
absolute values. In this case, it easier to proceed...

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