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Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15T
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Which of the following is correct for the given rational func. Show work 

(3x – 1)(x+1)
f(x) =
(2.x – 1)(x + 2)
-
I. It has vertical asymptotes of x =
1
-2 and x =
2
II. Its horizontal asymptote is y = 3.
III. Its y-intercept is at (0, ).
A. Ι only
В. II only
C. III only
D. I and II only
E. I and III only
F. II and III only
G. I, II, and III
H. None of these
Transcribed Image Text:(3x – 1)(x+1) f(x) = (2.x – 1)(x + 2) - I. It has vertical asymptotes of x = 1 -2 and x = 2 II. Its horizontal asymptote is y = 3. III. Its y-intercept is at (0, ). A. Ι only В. II only C. III only D. I and II only E. I and III only F. II and III only G. I, II, and III H. None of these
Expert Solution
Concept

Vertical Asymptotes:-

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)

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