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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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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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