Stitz-Zeager_College_Algebra_e-book

Compare and contrast their features which features

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Unformatted text preview: correspond to the x-values where the graph of y = h(x) is above the x-axis; the intervals on which h(x) < 0, or (−) correspond to where the graph is below the x-axis. y 8 7 6 5 4 3 (+) 1 −4 −3 −2 −1 (−) 0 (+) −1 11 2 2 3 4 1 2 (+) 1 x −2 −3 −4 −5 −6 As we examine the graph of y = h(x), reading from left to right, we note that from (−∞, −1), 1 2 Recall that, for our purposes, this means the graphs are devoid of any breaks, jumps or holes Another result from Calculus. 4.2 Graphs of Rational Functions 247 the graph is above the x-axis, so h(x) is (+) there. At x = −1, we have a vertical asymptote, at which point the graph ‘jumps’ across the x-axis. On the interval −1, 1 , the graph is below the 2 x-axis, so h(x) is (−) there. The graph crosses through the x-axis at 1 , 0 and remains above the 2 x-axis until x = 1, where we have a ‘hole’ in the graph. Since h(1) is undefined, there is no sign 1 here. So we have h(x) as (+) on the interval 2 , 1...
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