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: 30

Answer

$$ y=\frac{8}{5-3x} $$ We find that: Asymptote: $y=0$ and $x=\frac{5}{3}$ $x$-intercept: non $y$ -intercept: $\frac{8}{5}$
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Work Step by Step

$$ y=\frac{8}{5-3x} $$ The function is undefined for $x=\frac{5}{3}$, so the line $x=\frac{5}{3}$ is a vertical asymptotic.. To find a horizontal asymptotic, let $x$ get larger and larger, so that $$ y=\lim _{x \rightarrow \infty} \frac{8}{5-3x} =0 $$ This means that the line $y=0 $ is a horizontal asymptotic. When $x=0 $ the y-intercept is $\frac{8}{5}$ So, Asymptotic: $y=0$ and $x=\frac{5}{3}$ $x$-intercept: non $y$ -intercept: $\frac{8}{5}$
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