Answered: 12. For each rational function, find…

12. For each rational function, find the domain, the intercepts, and any verti- cal or horizontal asymptote. 2x2 + 4x 2x2 – 5x +3 g(x) = f(x) = x2 – 2x – 8 3x2 – 2x – 1'

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 51E

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Question

12. For each rational function, find the domain, the intercepts, and any verti-
cal or horizontal asymptote.
2x2 + 4x
2x2 – 5x +3
g(x) =
f(x) =
x2 – 2x – 8
3x2 – 2x – 1'

Expert Solution

Step 1

The given rational function can be simplified as follows.

2х2 +4х
f (x) =
х? — 2х —8
2x(x+2)
х? — 4х + 2х —8
2x (х +2)
x(х- 4) +2 (х-4)
2x (х+2)
(x+2)(х-4)

Step 2

Domain ‘D’ for the given function can be determined as to be.

Step 3

Intercepts for the given function can be determined as.

Step 4

Vertical asymptotes can be determined to be as.

Step 5

Horizontal asymptotes can be determined to be.

2x
lim
= 2
(x-4)
2x
lim
= 2
(x – 4)
y = 2
||
||

Step by step

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