# f(x)= (x^2 +10x +6)/(x+9)Given the rational function: (a) state the domain. (b) find the vertical and horizontal asymptotes, if any. (c) find the oblique asymptotes, if any. (d) graph of this...

f(x)= (x^2 +10x +6)/(x+9)

Given the rational function:

(a) state the domain.

(b) find the vertical and horizontal asymptotes, if any.

(c) find the oblique asymptotes, if any.

(d) graph of this function.

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Expert Answers

rcmath | Certified Educator

`x+9!=0 => x!=-9`

**Thus the domain is **`(-oo,-9)U(-9,oo)`

The same value that is excluded from the domain will give you the vertical asymptote, thus **x=-9 is vertical asymptote.**

This function has no horizontal asymptote.

To obtain the oblique asymptote, we can perform the long devision this will give us `(x^2+10x+6)/(x+9)=x+1+(-3)/(x+9)`

Hence the **oblique asymptote is y=x+1**