Given vertical asymptotes x = 2 and x = -5 .
Therefore Factors of denominator (x-2)(x+5).
x-intercepts (-1,0) and (1,0) .
Therefore factors of (x+1)(x-1).
So far we got rational function = [tex]\frac{(x+1)(x-1)}{(x-2)(x+5)}[/tex].
Now, we are given horizontal asymptote at y = 9.
Multiplying above express by 9 on the top, we get
[tex]f(x)=\frac{9(x+1)(x-1)}{(x-2)(x+5)}[/tex].
