Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 2 - Nonlinear Functions - 2.3 Polynomial and Rational Functions - 2.3 Exercises - Page 75: 29


$$ y=\frac{2}{3+2x} $$ We find that: Asymptotic : $ y=0 $ and $x=-\frac{3}{2}$ $x$-intercept: non $y$-intercept: $\frac{2}{3}$

Work Step by Step

$$ y=\frac{2}{3+2x} $$ The function is undefined for $x=-\frac{3}{2}$, so the line $x=-\frac{3}{2}$, is a vertical asymptotic.. To find a horizontal asymptotic, let $x$ get larger and larger, so that $$ y=\lim _{x \rightarrow \infty} \frac{2}{3+2x}=0 $$ This means that the line $y=0 $ is a horizontal asymptotic. When $x=0 $ the y-intercept is $\frac{2}{3}$. So , Asymptotic : $ y=0 $ and $x=-\frac{3}{2}$ $x$-intercept: non $y$-intercept: $\frac{2}{3}$
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