You can put this solution on YOUR website! Graph the rational function and show all asymptotes, zeros and intercepts
R(x) = (3x^2-12)/(x^2-x-20)
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Horizontal Asymptotes:HA
When degree of numerator and denominator the same, divide the lead coefficient of the numerator by the lead coefficient of the denominator:
HA: 3/1=3
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Vertical Asymptotes: VA
Set denominator=0, then solve for x-values which make the function undefined.
x^2-x-20
(x-5)(x+4)
VA: x=5 and x=-4
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Zeros:(x-intercepts)
set y=0
3x^2-12=0
x^2=4
x=±2
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y-intercept
set x=0
(3x^2-12)/(x^2-x-20)
-12/-20=3/5=.6
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number line:
<...+...-4....-....-2...+....2....-....5....+....>
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see graph below:
(