Question 390783
Whoa, STUDENT, you ask too much, he he. But I'll show you one rational function that will satisfy your conditions. Maybe some other tutor will show you the graphing/long dividing parts.  

{{{f(x) = ((3x -6)(x+1)^2)/((2x-1)(x+3))}}}.

The degree of the top polynomial is 3, the bottom, 2, so after long division, the quotient is a linear function whose slope is 3/2.  (You can even determine this by inspection!)
The roots of the function (which correspond to the x-intercepts) are 2 (multiplicity 1), and -1 (multiplicity 2).
The roots OF THE BOTTOM EXPRESSION, 1/2 and -3, yield the vertical asymptotes.  The equations are exactly x = 1/2 and x = -3.