## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 4 - 4.1 - Rational Functions and Asymptotes - 4.1 Exercises - Page 315: 15

#### Answer

Vertical Asymptote: x = 5 Horizontal Asymptote: y = -1

#### Work Step by Step

A graph has a vertical asymptote where the denominator is equal to 0. A graph has a horizontal asymptote based on the difference in degrees of the numerator and denominator. If the numerator has a larger degree than the denominator, then the graph has no horizontal asymptote. If the denominator has a larger degree than the numerator, then y = 0 is a horizontal asymptote. If the denominator has the same degree as the numerator, then the horizontal asymptote is the leading coefficient of the numerator divided by the leading coefficient of the denominator. f(x) = $\frac{5 + x}{5 - x}$ Vertical Asymptote: 5 - x = 0 x = 5 x = 5 is a Vertical asymptote because it makes the denominator 0. Horizontal Asymptote: Since both the numerator and denominator have a degree of 1, the horizontal asymptote is the ratio of the leading coefficients. y = $\frac{1}{-1}$ = -1 y = -1 is a horizontal asymptote.

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