**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} $

Answered: 2. For each rational function, give the…

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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Question

**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