# How do you identify all asymptotes for #f(x)=(1+3x^2-x^3)/x^2#?

##### 1 Answer

#### Explanation:

First of all one need to see, whether there areany holes or not, i.e. those values of

Further, if denominator can be factorized, we have vertical asymptotes. If factors are

Horizontal asymptotes appear when degree of numerator and denominator are same. It is not so. However as degree of numerator is just one more than that of denominator, there is a slant or oblique asymptote.

Observe that

and as

Hence slanting asymptote is

graph{(1+3x^2-x^3)/x^2 [-19.17, 20.83, -1.44, 18.56]}