Stitz-Zeager_College_Algebra_e-book

# Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: x2x−7 6 as x → ∞, we imagine −x− substituting x = 1 billion and, going through the usual mental routine, ﬁnd x−7 ≈ very small (+) x2 − x − 6 Hence, g (x) ≈ 2 − very small (+), in other words, the graph of y = g (x) is just below the line y = 2 as x → ∞. On y = g (x), we have (again, without labels on the x-axis) y 1 x −1 6. Finally we construct our sign diagram. We place an ‘ ’ above x = −2 and x = 3, and a ‘0’ above x = 5 and x = −1. Choosing test values in the test intervals gives us f (x) is (+) on 2 5 5 the intervals (−∞, −2), −1, 2 , and (3, ∞), and (−) on the intervals (−2, −1) and 2 , 3 . As we piece together all of the information, we note that the graph must cross the horizontal asymptote at some point after x = 3 in order for it to approach y = 2 from underneath. This is the subtlety that we would have missed had we skipped the long division and subsequent end behavior analysis. We can, in fact, ﬁnd exactly when the graph crosses y = 2. As a result of the long divisi...
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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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