How do you graph f(x)=(2x^3+x^2−8x−4)/(x^2−3x+2) using holes, vertical and horizontal asymptotes, x and y intercepts?

ajakanvao

ajakanvao

Answered question

2022-11-14

How do you graph f ( x ) = 2 x 3 + x 2 - 8 x - 4 x 2 - 3 x + 2 using holes, vertical and horizontal asymptotes, x and y intercepts?

Answer & Explanation

retalibry9

retalibry9

Beginner2022-11-15Added 16 answers

f ( x ) = x 2 ( 2 x + 1 ) - 4 ( 2 x + 1 ) ( x - 2 ) ( x - 1 ) = ( x 2 - 4 ) ( 2 x + 1 ) ( x - 2 ) ( x - 1 ) = ( x - 2 ) ( x + 2 ) ( 2 x + 1 ) ( x - 2 ) ( x - 1 ) =

hole: x=2

= ( x + 2 ) ( 2 x + 1 ) ( x - 1 ) = 2 x 2 + 5 x + 2 x - 1 = f ( x )

vertical asymptote: x=1

horizontal asymptotes:
lim x + f ( x ) = +
lim x - f ( x ) = -
none

graph{(2x^3+x^2-8x-4)/(x^2-3x+2) [-200, 200, -150, 150]}

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