We are asked to graph the function ` y=(x^2+11x+18)/(2x+1) ` :

Factoring the numerator yields:

`y=((x+9)(x+2))/(2x+1) `

There is a vertical asymptote at x=-1/2. The x-intercepts are at -2,-9.

There is no horizontal asymptote as the degree of the numerator is greater than the degree of the denominator. The slant asymptote, found by division, is y=1/2x+21/4.

The graph: