SOLUTION: Write a rational function that has the following attributes: Vertical asymptote: x=-1, x=2 Horizontal asymptote: y=-2 x-intercept: x=3, x=-2

Algebra ->  Rational-functions -> SOLUTION: Write a rational function that has the following attributes: Vertical asymptote: x=-1, x=2 Horizontal asymptote: y=-2 x-intercept: x=3, x=-2       Log On


   

Question 694889: Write a rational function that has the following attributes:
Vertical asymptote: x=-1, x=2
Horizontal asymptote: y=-2
x-intercept: x=3, x=-2
Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
Vertical asymptotes occur when denominator is zero
so Vertical asymptote at x=-1, x=2 would need factors +%28x%2B1%29%28x-2%29+ in the denominator
so we are looking for a function of the form +g%28x%29%2F%28x%2B1%29%28x-2%29+
x-intercept x=3, x=-2 would need factors +%28x-3%29%28x%2B2%29+ in the numerator
so we are looking for a function of the form +h%28x%29%28x-3%29%28x%2B2%29%2F%28x%2B1%29%28x-2%29+
Finally we want a Horizontal asymptote at y=-2, this would require y ~ -2 as +x-%3Einfinity+, which leads to the function
+-2%28x-3%29%28x%2B2%29%2F%28x%2B1%29%28x-2%29+