Graph all asymptotes of the rational function.x++6x+ 1S(x) =x-28-7+6-5-43.2--6-5-4-3-1-2--3.-4--5--6--7.i 图

Answered: Graph all asymptotes of the rational…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Graph all asymptotes of the rational function.
x++6x+ 1
S(x) =
x-2
8-
7+
6-
5-
4
3.
2-
-6
-5
-4
-3
-1
-2-
-3.
-4-
-5-
-6-
-7.
i 图

Expert Solution

Step 1

$G i v e n t h a t f (x) = \frac{- x^{2} + 6 x + 1}{x - 2} S o l u t i o n : H o r i z o n t a l a s y m p t o t e s i f d e g r e e o f n u m e r a t o r i s g r e a t e r t h e n d e g r e e o f d e n o m i n a t o r t h e n n o h o r i z o n t a l a s y m p t o t e s s o, g i v e n f u n c t i o n n o h o r i z o n t a l a s y m p t o t e s v e r t i c a l a s y m p t o t e s : i f f (x) = \frac{p (x)}{q (x)} t h e n p u t q (x) = 0 a n d s o l v e f o r x . x - 2 = 0 x = 2 v e r t i c a l a s y m p t o t e s$