a b and c Consider the following rational function:,п —anx" + an – 1x"-1+ a1x + ao•..f(x)1bmxm + bm – 1x™-+... + bịx + bowhere the numerator and denominator is written arepolynomials of degree n and m, respectively. Foreach of the following, select all correct answers.Which of the following conditions means that fmust:a. have a horizontal asymptote at y = 0?Om = nOm < nOm > nb. have a horizontal asymptote at y = a forsome a + 0?Um = nOm < nOm > nc. not have a horizontal asymptote?Om =Um < nOm > n

Answered: Consider the following rational…

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

a b and c

Consider the following rational function:
,п —
anx" + an – 1x"-1
+ a1x + ao
•..
f(x)
1
bmxm + bm – 1x™-
+
... + bịx + bo
where the numerator and denominator is written are
polynomials of degree n and m, respectively. For
each of the following, select all correct answers.
Which of the following conditions means that f
must:
a. have a horizontal asymptote at y = 0?
Om = n
Om < n
Om > n
b. have a horizontal asymptote at y = a for
some a + 0?
Um = n
Om < n
Om > n
c. not have a horizontal asymptote?
Om =
Um < n
Om > n

Expert Solution

Step 1

Recall:

$Horizontal asymptotes of a rational function : Consider the rational function f (x) = \frac{{ax}^{n} + . . .}{{bx}^{m} + . . .} where' n' and' m' is the largest exponent in the numerator and denominator . (1) If n < m, then the x - axis is the horizontal asymptote . (2) If n = m, then the line y = \frac{a}{b} is the horizontal asymptote . (3) If n > m there will be no horizontal asymptote .$