SOLUTION: Graph the rational function and show all asymptotes, zeros and intercepts R(x) = 3x^2-12/x^2-x-20

Question 709594: Graph the rational function and show all asymptotes, zeros and intercepts
R(x) = 3x^2-12/x^2-x-20
Answer by lwsshak3(11628) (Show Source): 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)
..
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
..
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
..
Zeros:(x-intercepts)
set y=0
3x^2-12=0
x^2=4
x=�2
..
y-intercept
set x=0
(3x^2-12)/(x^2-x-20)
-12/-20=3/5=.6
..
number line:
<...+...-4....-....-2...+....2....-....5....+....>
..
see graph below:

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