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Identify the y-intercepts, horizontal or oblique asymptotes, holes, x-inteceps and vertical asymptotes of f(x) f(x) = 2x3+x2- 25x+12 / (4x2-16x+12)

Identify the y-intercepts, horizontal or oblique asymptotes, holes, x-inteceps and vertical asymptotes of f(x) f(x) = 2x3+x2- 25x+12 / (4x2-16x+12)

Calculus: Early Transcendentals
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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Identify the y-intercepts, horizontal or oblique asymptotes, holes, x-inteceps and vertical asymptotes of f(x)

f(x) = 2x3+x2- 25x+12 / (4x2-16x+12)

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.

y=\frac{2x^3+x^2-25x+12}{4x^2-16x+12}.................(1)

write the factored form of the numerator

2x^3+x^2-25x+12

here we have

a_0=12,\:\quad a_n=2

\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:3,\:4,\:6,\:12

\mathrm{The\:dividers\:of\:}a_n:\quad 1,\:2

rational\:\:numbers: \pm \left ( \frac{1,\:2,\:3,\:4,\:6,\:12}{1,\:2} \right )

here x=3 is a root, so take the synthetic division

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