Stitz-Zeager_College_Algebra_e-book

F x x 4 5 a x 1 or x 9 2 c x 0 or x

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Unformatted text preview: Rewriting the formula for i(x) without absolute values gives i(x) = 4 − 2(−(3x + 1)), if 3x + 1 < 0 = 4 − 2(3x + 1), if 3x + 1 ≥ 0 6x + 6, if x < − 1 3 −6x + 2, if x ≥ − 1 3 The usual analysis near the trouble spot, x = − 1 gives the ‘corner’ of this graph is − 1 , 4 , 3 3 and we get the distinctive ‘∨’ shape: 2.2 Absolute Value Functions 131 y 3 2 1 −1 1 x −1 −2 −3 i(x) = 4 − 2|3x + 2| The domain of i is (−∞, ∞) while the range is (−∞, 4]. The function i is increasing on 1 1 −∞, − 3 and decreasing on − 3 , ∞ . The relative maximum occurs at the point − 1 , 4 3 and the relative and absolute maximum value of i is 4. Since the graph of i extends downwards forever more, there is no absolute minimum value. As we can see from the graph, there is no relative minimum, either. Note that all of the functions in the previous example bear the characteristic ‘∨’ shape as the graph of y = |x|. In fact, we could have graphed all o...
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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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