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`y=(x^2+11x+18)/(2x+1)` Graph the function.

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:


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