Stitz-Zeager_College_Algebra_e-book

Stitz-Zeager_College_Algebra_e-book

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online