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2. For each rational function, give the equation(s) of each asymptote. If there are none, then say "None." A. f(x) B. g(x) = = 7x² - 6x 6 5x² - 3 - 2x³ + 13x² + 16x x2+5 +6 - 3

2. For each rational function, give the equation(s) of each asymptote. If there are none, then say "None." A. f(x) B. g(x) = = 7x² - 6x 6 5x² - 3 - 2x³ + 13x² + 16x x2+5 +6 - 3

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem 2: Asymptotes of Rational Functions** For each rational function, give the equation(s) of each asymptote. If there are none, then say "None." **A.** \( f(x) = \frac{7x^2 - 6x - 6}{5x^2 - 3} \) **B.** \( g(x) = \frac{2x^3 + 13x^2 + 16x - 3}{x^2 + 5x + 6} \)
Transcribed Image Text:**Problem 2: Asymptotes of Rational Functions** For each rational function, give the equation(s) of each asymptote. If there are none, then say "None." **A.** \( f(x) = \frac{7x^2 - 6x - 6}{5x^2 - 3} \) **B.** \( g(x) = \frac{2x^3 + 13x^2 + 16x - 3}{x^2 + 5x + 6} \)
Expert Solution
Step 1: concept

Vertical asymptotes:

If h left parenthesis x right parenthesis equals fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction is a rational function then the vertical asymptotes are at the points where g(x)=0.

if g(x)=0 at x=a then the equation of vertical asymptote is x=a.

Horizontal asymptotes :

If h left parenthesis x right parenthesis equals fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction is a Rational function where the degree of f(x) is N and degree of denominator is D and

  1. if N<D the horizontal asymptote is y=0.
  2. if N=D, then the horizontal asymptote is y= ratio of leading coefficients.
  3. if N>D, then horizontal asymptote does not exist.
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