Consider a rational function p(x) with vertical asymptotes at x=3 and x=-3. The graph of p(x) shows a horizontal asymptote at y=4, and a y intercept at the point (0,-1). Write the function p(x)

Question

Consider a rational function p(x) with vertical asymptotes at x=3 and x=-3. The graph of p(x) shows a horizontal asymptote at y=4, and a y intercept at the point (0,-1).  Write the function p(x)

anonymous · Answer

denominator must have zeros at $3$ and $-3$ so it could be 
$$(x+3)(x-3)=x^2-9$$

anonymous · Answer

horizontal asymptote at $y=4$ means the numerator must have the same degree as the denominator and leading coefficient of 4, so it could be for example $4x^2$

anonymous · Answer

but since $f(0)=-1$ it cannot be $4x^2$ but it could be $4x^2-1$

anonymous · Answer

try 
$$p(x)=\frac{4x^2-1}{x^2-9}$$ 
weird that they call it $p$ since it is not a polynomial...