Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.6 - Rational Expressions - 3.6 Exercises - Page 309: 85

Answer

See upper graph, vertical asymptote $x=3$ x-intercepts $1.6,2.7$ y-intercepts $-2$ local minima $(0.6,-2.3),(3.4,54.3)$, local maxima $(-0.4,-1.8),(2.4,3.8)$ end behaviors: $y=x^3$, see lower graph.

Work Step by Step

See upper graph, and based on the curve, we have vertical asymptotes, $x=3$ x-intercepts, $1.6,2.7$ y-intercepts $-2$ local minima $(0.6,-2.3),(3.4,54.3)$, local maxima $(-0.4,-1.8),(2.4,3.8)$ end behaviors: use long division (shown in the middle of the figure), we can find the quotient as $y=x^3$ which has the same end behavior as the rational function, see lower graph.
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