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: 73

Answer

Slant asymptotes: $y=x+8$ Vertical asymptote: $x=3$ See graph.

Work Step by Step

1. To find the slant asymptote, we use synthetic division as shown in the figure. 2. Based on the division results, we get $r(x)=x+8+\frac{28}{x-3}$ 3. We can identify the slant asymptotes as $y=x+8$ (quotient of the division) 4. The vertical asymptote can be found as $x=3$ (zero of the denominator) 5. The graph of the function is shown in the figure.
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