Write an equation of a rational function with these conditions: No Vertical Asymptote Horizontal Asymptote at y=5 Y-intercept at (0,3)

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 .

The function has a horizontal Asymptote at y=5. So the polynomial of the numerator would have a type like  . 

So from these data we can say the function is;

...

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 .

The function has a horizontal Asymptote at y=5. So the polynomial of the numerator would have a type like  . 

So from these data we can say the function is;

It is given that at x = 0 then y = 3.

So a and b can be any rational value where .

A simple form of the answer would be at a = 1 and b = 0;

So the answer can be given as;