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

##### 1 Answer

There is a hole at

A vertical asymptote is

The slant asymptote is

There is no horizontal asymptote.

#### Explanation:

Let's factorise the denominator

Let's factorise the numerator

Therefore,

There is a hole at

The domain of

As we cannot divide by

A vertical asymptote is

As the degree of the numerator is

Let's do a long division

So,

The slant asymptote is

To calculate the limit, we take the terms of highest degree.

There is no horizontal asymptote.

graph{(y-(x^2+x+1)/(2x+2))(y-x/2)=0 [-5.542, 5.553, -2.783, 2.766]}