How do you find all the asymptotes for function #f(x) = (2x^2+3x+8)/(x+3)#?
There are three types of asymptotes.
Vertical asymptotes are indicated by denominator. Here we have
Horizontal asymptotes in such cases (algebraic expressions) are there when degree of numerator is equal to that of denominator. Here it is not so we do not a horizontal asymptote. Stll assume numerator as only
Here we have
Hence we have a slanting or oblique asymptote
It is apparent that we have this only when degree of numerator is one more than that of denominator.