Stitz-Zeager_College_Algebra_e-book

# If a 0 then ax h2 is positive and so y ax h2 k

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Unformatted text preview: that the only piece which contains a variable is g (x) = 2x for −2 ≤ x &lt; 3. Solving 2x = 0 gives x = 0. Since x = 0 is in the interval [−2, 3), we keep this solution and have (0, 0) as our only x-intercept. Accordingly, the y -intercept is also (0, 0). To graph g , we start with x &lt; −2 and graph the horizontal line y = −4 with an open circle at (−2, −4). For −2 ≤ x &lt; 3, we graph the line y = 2x and the point (−2, −4) patches the hole left by the previous piece. An open circle at (3, 6) completes the graph of this part. Finally, we graph the horizontal line y = 6 for x ≥ 3, and the point (3, 6) ﬁlls in the open circle left by the previous part of the graph. The ﬁnished graph is y 6 5 4 3 2 1 −4 −3 −2 −1 1 2 3 4 x −1 −2 −3 −4 g (x) = |x + 2| − |x − 3| + 1 The domain of g is all real numbers, (−∞, ∞), and the range of g is all real numbers between −4 and 6 inclusive, [−4, 6]. The function is increasing on [−2, 3] and constant on (−∞, −2] and [3, ∞). The relative minimum value of f is 4 which matches...
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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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