Answer
$f(x)=\frac{3(x-2)(x+1)}{(x+5)(x-6)}$
Work Step by Step
If a function crosses/touches the x-axis at $x=a$ then in its numerator, $(x-a)$ must appear because that will make the value of the function $0$ there (because the x-axis is $y=0$).
If a function has a vertical asymptote at $x=b$ then in its denominator, $(x-b)$ must appear because that will make the value of the function undefined there which is necessary for a vertical asymptote.
We have to multiply the numerator by $c$ if $y=c$ is a horizontal asymptote. $f(x)=\frac{3(x-2)(x+1)}{(x+5)(x-6)}$ My classmate got the same function.
