# How do you identify all asymptotes or holes for #f(x)=(x^2+11x+18)/(2x+1)#?

##### 1 Answer

Dec 16, 2016

There is no hole. We have vertical asymptote at

#### Explanation:

Let us examine

As

=

As a common factor cannot be crossed out from both the numerator and the denominators, we do not have a hole in

It is also apparent that as

and as we have

Hence, we have a vertical asymptote at

Further,

=

=

Hence, as

and we have an oblique asymptote at

graph{(y-(x^2+11x+18)/(2x+1))(x+1/2)(2x-4y+21)=0 [-21.08, 18.92, -5.32, 14.68]}