Question 757508: y=(x^2+3x+2)/(9-x^2)
please help me find the VA, HA, graph, domain and range. Thank you so much! :)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! y=(x^2+3x+2)/(9-x^2)
please help me find the VA, HA, graph, domain and range.
***
y=(x^2+3x+2)/(9-x^2)=(x+2)(x+1)/(3+x)(3-x)
horizontal asymptote: y=-1 (Rule: when degree of denominator same as that of numerator, divide coefficients of the higher degree terms. In this case,1/-1=-1
..
Vertical asymptotes:
set denominator =0, then solve for x
9-x^2=0
(3+x)(3-x)=0
x=-3, 3
VA: x=-3, and x=3
number line:
<...-...-3...+...-2...-...-1...+...3...-....>
Domain: (-∞,-3) U (-3,-2) U (-2,-1) U (-1,3) U (3,∞) (between x=-2 and x=-1, function goes negative a small amount which cannot be seen on the graph)
Range: (-∞,-1) U (0-,∞)
see graph below as a visual check:
|
|
|
