Rational Function

Question

Find a rational function that represents a graph that has a vertical asymptote at x=2 and x= -3 and a horizontal azymptote at y=0.

 

the answer is f(x)= (x-4)/(x²+x-6) 

 

I understand how the denominator was found but I am unsure about the numerator. 

Thank you for the help 

Answer 1

Since we have a rational function with horizontal asymptote at y=0, the degree of the numerator need to be less than 2. That is why your answer works. But that answer is not unique. Any rational function with ax+b in the numerator also works.