Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let r(x) = p(x)/q(x), where p & q are polynomials of degree n & m, respectively. We can express p and q as: a/ Assume p and q have no common zeros. Where do the vertical asymptotes of r(x) occur? Explain in terms of p(x) and/or q(x). b/ As x → −∞ (or x → ∞), what term dominates the behavior of p(x)? c/ As x → −∞ (or x → ∞), what term dominates the behavior of q(x)?

Let r(x) = p(x)/q(x), where p & q are polynomials of degree n & m, respectively. We can express p and q as: a/ Assume p and q have no common zeros. Where do the vertical asymptotes of r(x) occur? Explain in terms of p(x) and/or q(x). b/ As x → −∞ (or x → ∞), what term dominates the behavior of p(x)? c/ As x → −∞ (or x → ∞), what term dominates the behavior of q(x)?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 54E
See similar textbooks
icon
Related questions
Question

Let r(x) = p(x)/q(x), where p & q are polynomials of degree n & m, respectively. We can express p and q as:

a/ Assume p and q have no common zeros. Where do the vertical asymptotes of r(x) occur? Explain in terms of p(x) and/or q(x).

b/ As x → −∞ (or x → ∞), what term dominates the behavior of p(x)?

c/ As x → −∞ (or x → ∞), what term dominates the behavior of q(x)?

We can express p and q as: p(x) Anx¹ + an_1x¹-1 + + ao and q(x) = bmxm + bm-1xm. + + bo where (i). all aj, b¡ are constants, (ii). m, n ≥ 0 are constant integers, and (iii). an, bm ‡ 0. =
Transcribed Image Text:We can express p and q as: p(x) Anx¹ + an_1x¹-1 + + ao and q(x) = bmxm + bm-1xm. + + bo where (i). all aj, b¡ are constants, (ii). m, n ≥ 0 are constant integers, and (iii). an, bm ‡ 0. =
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 13 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS