SOLUTION: make a graph of f(x)= 3x^2+3x-6/x^2+x-12. list all asymptotes, domains, and the x,y intercepts.

Algebra ->  Trigonometry-basics -> SOLUTION: make a graph of f(x)= 3x^2+3x-6/x^2+x-12. list all asymptotes, domains, and the x,y intercepts.      Log On


   

Question 1137489: make a graph of f(x)= 3x^2+3x-6/x^2+x-12. list all asymptotes, domains, and the x,y intercepts.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

make a graph of

f%28x%29=+%283x%5E2%2B3x-6%29%2F%28x%5E2%2Bx-12%29
f%28x%29=+%283x%5E2-3x%2B6x-6%29%2F%28x%5E2-3x%2B4x-12%29
f%28x%29=+%28%283x%5E2-3x%29%2B%286x-6%29%29%2F%28%28x%5E2-3x%29%2B%284x-12%29%29
f%28x%29=+%283x%28x-1%29%2B6%28x-1%29%29%2F%28x%28x-3%29%2B4%28x-3%29%29
f%28x%29=+%28%283x%2B6%29%28x-1%29%29%2F%28%28x+%2B+4%29+%28x+-+3%29%29

asymptotes:
Horizontal asymptote:
%283+x%5E2+%2B+3+x+-+6%29%2F%28x%5E2+%2B+x+-+12%29-%3E3 as+x-> ±infinity
=>horizontal asymptote is y=3

Vertical asymptotes:
%283+x%5E2+%2B+3+x+-+6%29%2F%28x%5E2+%2B+x+-+12%29-> ± infinity as x-%3E-4
%283+x%5E2+%2B+3+x+-+6%29%2F%28x%5E2+%2B+x+-+12%29-> ± infinity as+x-%3E3
=> vertical asymptotes are x=-4 and x=3

domain:
{ x element R : x%3C%3E-4 and x%3C%3E3 }

the x intercepts:
%283x%2B6%29%28x-1%29=0
if %283x%2B6%29=0=>3x=-6=>x=-2
if %28x-1%29=0=>x=1
the x intercepts:(+1,0) and (-2,0)

the y intercept:
f%280%29=+%283%2A0%5E2%2B3%2A0-6%29%2F%280%5E2%2B0-12%29=-6%2F-12=1%2F2
(0, 1%2F2)