The function has no vertical Asymptote means the denominator does not equate to 0 at any value of x. In other words the polynomial should not have real roots. A simple form of this type function of function would be `ax^2+1` .
The function has a horizontal Asymptote at y=5. So the polynomial of the numerator would have a type like `5x^2+bx+c` .
So from these data we can say the function is;
`f(x) = (5x^2+bx+c)/(ax^2+1)`
It is given that at x = 0 then y = 3.
`3 = c/1`
`c = 3`
`f(x) = (5x^2+bx+3)/(ax^2+1)`
So a and b can be any rational value where `a!=0` .
A simple form of the answer would be at a = 1 and b = 0;
So the answer can be given as;