Question 527008: zeroes, vertical,horizontal, or oblique asymptotes of
(4x^2+12x+9)/(x^2-6x+5)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! zeroes, vertical,horizontal, or oblique asymptotes of
(4x^2+12x+9)/(x^2-6x+5)
**
(4x^2+12x+9)/(x^2-6x+5)
(2x+3)^2/(x-1)(x-5)
..
y-intercept
set x=0
y=9/5=1.8
..
x-intercepts (zeros)
set y=0
0=(2x+3)^2
x=-3/2 (mult. 2)
..
horizontal asymptote:
When degree of numerator and denominator are the same, divide the lead coefficients of top and bottom=4/1=4=horizontal asymptote.
..
vertical asymptotes
set denominator=0, and solve for x
x-1=0
x=1
and
x-5=0
x=5
Vertical asymptotes:
x=1, and x=5
There are no oblique asymptotes
..
number line
<...+....-3/2....+.....1.....-.....5......+......>
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