SOLUTION: Gragh g: g(x)=(-2x^2+18)/(3x^2-12)

Question 511521: Gragh g: g(x)=(-2x^2+18)/(3x^2-12)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Gragh g: g(x)=(-2x^2+18)/(3x^2-12)
**
g(x)=(-2x^2+18)/(3x^2-12)
=-2[x^2-9]/3[x^2-4]
=-2[(x+3)(x-3)]/3[(x+2)(x-2)]
..
y-intercept
set x=0
g(x)=18/-12=-3/2
..
x-intercepts
set y=0
-2x^2+18=0
-2(x^2-9)=0
-2(x+3)(x-3=0
x=-3
or
x=3
..
Horizontal Asymptote (HA)
When degree of numerator same as that of denominator,
HA=leading coefficient of numerator/leading coefficient of denominator
HA=y=-2/3
..
Vertical Asymptote (VA)
set denominator=0
(3x^2-12)=0
3(x+2)(x-2)=0
x=-2
and
x=2
..
number line:
<....+....-3....-....-2....+....2....-....3....+....>
see graph below as a visual check on the answers above:
..

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