# How do you find the vertical, horizontal and slant asymptotes of: # f(x)=((x-2)^2(2x+5)) /( (x-3)^2(x-2))#?

##### 1 Answer

Vertical asymptote at

Hole at

No slant asymptote

Horizontal asymptote at

#### Explanation:

**Holes** come when you can cancel a term because it is in the numerator and denominator:

**Vertical asymptotes** come from setting all terms except the term that causes the hole

**Horizontal asymptotes** are determined by the degrees of the numerator and denominator:

If

In the function:

so there is a horizontal asymptote at

To have a **slant asymptote** :

To summarize:

Vertical asymptote at

Hole at

No slant asymptote

Horizontal asymptote at