2x – 1 1. Consider the function y x2 +4 (a) State all vertical asymptotes, if they exist. (b) State all horisontal asymptotes, if they exist.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 8E
icon
Related questions
Question
2х — 1
1. Consider the function y =
x2 + 4
(a) State all vertical asymptotes, if they exist.
(b) State all horisontal asymptotes, if they exist.
Transcribed Image Text:2х — 1 1. Consider the function y = x2 + 4 (a) State all vertical asymptotes, if they exist. (b) State all horisontal asymptotes, if they exist.
Expert Solution
Concept

Vertical Asymptotes:-

Are vertical lines which correspond to the zeroes of the denominator of a rational function.

To find horizontal asymptotes:

 

If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).

If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.

If the degrees of the numerator and denominator are the same, the horizontal asymptote equals the leading coefficient (the coefficient of the largest exponent) of the numerator divided by the leading coefficient of the denominator

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Asymptote
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning