College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 3, Polynomial and Rational Functions - Section 3.6 - Rational Functions - 3.6 Exercises - Page 344: 30

Answer

x-intercepts: $\qquad -2$ and $2.$ y-intercept: $\qquad -6$. Vertical asymptotes: $\qquad $ none. Horizontal asymptote: $\qquad y=2$

Work Step by Step

The graph crosses the x-axis at ($-2,0$) and at ($2,0$) x-intercepts: $-2$ and $2.$ The graph crosses the y-axis at ($0.-6$) y-intercept: $-6$ Vertical lines are where the function is undefined, and the graph rises/falls without bound on either side. Thus, there are none (no vertical asymptotes.) The horizontal line, which the graph approaches when $x\rightarrow\pm\infty,$ is $y=2$ (the horizontal asymptote).
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