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

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) (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)
---
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)
---
x-intercept: 5
If y = 0 , then x = 5.
From (ii) we get
(iii)
cross multiply to get
5a+b = 0
solving for a , we get
(iv)
---
f (6) = 1
means that if x = 6, then y = 1.
From (i) and (iv) we get
(vi)
cross multiplying we get
(vii)
multiply by common denominator of 5, we get
(viii)
solving for b, we get
(ix)
This means that

and our equation is

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