SOLUTION: Hi. I am having trouble with the following problem. I understand everything except for the x-intercept part. I would greatly appreciate your help, Thanks in advance. Find an eq

Algebra ->  Rational-functions -> SOLUTION: Hi. I am having trouble with the following problem. I understand everything except for the x-intercept part. I would greatly appreciate your help, Thanks in advance. Find an eq      Log On


   

Question 269853: Hi. I am having trouble with the following problem. I understand everything except for the x-intercept part. I would greatly appreciate your help,
Thanks in advance.
Find an equation of a rational function f that satisfies the conditions:
vertical asymptotes: x = - 2, x = 0
horizontal asymptote: y = 0
x-intercept: 5; f (6) = 1
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation of a rational function f that satisfies the conditions:
vertical asymptotes: x = - 2, x = 0
we can write a general form as
(i) y+=+%28ax%2Bb%29%2F%28x%28x%2B2%29%29%29
---
horizontal asymptote: y = 0
This means as x approaches infinity, then the function approaches zero. This happens when the degree of the numerator is less than the degree of the denominator
we keep our function at
(ii) y+=+%28ax%2Bb%29%2F%28x%28x%2B2%29%29%29
---
x-intercept: 5
If y = 0 , then x = 5.
From (ii) we get
(iii)%285a%2Bb%29%2F%285%285%2B2%29%29+=+0
cross multiply to get
5a+b = 0
solving for a , we get
(iv) a+=+-b%2F5
---
f (6) = 1
means that if x = 6, then y = 1.
From (i) and (iv) we get
(vi) 1+=+%286%28-b%2F5%29%2Bb%29%2F%286%286%2B2%29%29%29
cross multiplying we get
(vii) 48+=+-6b%2F5+%2B+b
multiply by common denominator of 5, we get
(viii) 240+=+-6b+%2B+5b
solving for b, we get
(ix) b+=+-240
This means that
a+=+48
and our equation is
y+=+%2848x-240%29%2F%28x%28x%2B2%29%29%29