Write a possible formula for the rational function with thes

Write a possible formula for the rational function with these properties:
a single zeros at 5 and 3;
a vertical asymptote at x = 9;
a horizontal asymptote at y = 3.
Factors should have the least degree possible.

Your formula should begin with y=.

Solution

a single zeros at 5 and 3 ----> numerator (x-5)(x-3)
a vertical asymptote at x = 9; ----> denominator (x-9)
a horizontal asymptote at y = 3.f(x) ---> The degree of terms needs to be same in both num. and den. to have

a horizontal asymtote.

So, denominator would have (x-9)^2

Further y = 3 is hor. asymtote

So, coefficient of highest term would be 7

So, f(x) = 7(x-5)(x-3)/(x-9)^2 . This fulfills all criteria