11. Consider the following rational functions: 2x 1 x + 27 x -- 9x x² + x - 6 x + 6x² + 9x r(x) s(x) t(x) u(x) w(x) x² - x-2 x² + 4 x + 2 x² - 25 x + 3 (a) Which of these rational functions has a horizontal asymptote? (b) Which of these functions has a slant asymptote? (c) Which of these functions has no vertical asymptote? (d) Which of these functions has a "hole"?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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11. Consider the following rational functions:
2x 1
x - 9x
X+27
3
-
r(x)
s(x)
t(x)
u(x)
x+ x- 6
w(x)
x' + 6x + 9x
x2 - x - 2
x² + 4
x² - 25
x+ 3
(a) Which of these rational functions has a horizontal asymptote?
(b) Which of these functions has a slant asymptote?
(c) Which of these functions has no vertical asymptote?
(d) Which of these functions has a "hole"?
Transcribed Image Text:11. Consider the following rational functions: 2x 1 x - 9x X+27 3 - r(x) s(x) t(x) u(x) x+ x- 6 w(x) x' + 6x + 9x x2 - x - 2 x² + 4 x² - 25 x+ 3 (a) Which of these rational functions has a horizontal asymptote? (b) Which of these functions has a slant asymptote? (c) Which of these functions has no vertical asymptote? (d) Which of these functions has a "hole"?
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