## Calculus with Applications (10th Edition)

Published by Pearson

# Chapter 2 - Nonlinear Functions - 2.3 Polynomial and Rational Functions - 2.3 Exercises - Page 75: 28

#### Answer

$$y=\frac{-1}{x+3}$$ The function is undefined for $x=-3$, so the line $x=-3$ is a vertical asymptotic.. To find a horizontal asymptotic, let $x$ get larger and larger, so that $$y=\lim _{x \rightarrow \infty}\frac{-1}{x+3}=0$$ This means that the line $y=0$ is a horizontal asymptotic. When $x=0$ the y-intercept is $-\frac{1}{3}$

#### Work Step by Step

$$y=\frac{-1}{x+3}$$ The function is undefined for $x=-3$, so the line $x=-3$ is a vertical asymptotic.. To find a horizontal asymptotic, let $x$ get larger and larger, so that $$y=\lim _{x \rightarrow \infty}\frac{-1}{x+3}=0$$ This means that the line $y=0$ is a horizontal asymptotic. When $x=0$ the y-intercept is $-\frac{1}{3}$

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