Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 4 - Polynomial and Rational Functions - 4.2 Properties of Rational Functions - 4.2 Assess Your Understanding - Page 198: 51

Answer

vertical asymptote $x=-\frac{1}{3}$, horizontal asymptote $y=\frac{2}{3}$, oblique asymptote $none$.

Work Step by Step

Step 1. Factor the function $Q(x)=\frac{2x^2-5x-12}{3x^2-11x-4}=\frac{(x-4)(2x+3)}{(x-4)(3x+1)}=\frac{2x+3}{3x+1}, (x\ne4)$, Step 2. we can find the vertical asymptote $x=-\frac{1}{3}$, Step 3. we can find the horizontal asymptote $y=\frac{2}{3}$, Step 4. we can find the oblique asymptote $none$.
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