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
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...
Related questions
Question

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
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Step 1: concept
Vertical asymptotes:
If 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 is a Rational function where the degree of f(x) is N and degree of denominator is D and
- if N<D the horizontal asymptote is y=0.
- if N=D, then the horizontal asymptote is y= ratio of leading coefficients.
- if N>D, then horizontal asymptote does not exist.
Step by step
Solved in 4 steps with 5 images
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