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.
`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