# How do you find all the asymptotes for function #y = x/(x-6) #?

##### 1 Answer

#### Explanation:

3 types of asymptotes : Vertical, horizontal and oblique.

**Vertical :**

The straight line

Let

The domain of f(x) is

We generally find a vertical asymptote in a rational function, when the value of denominator is equal to 0 *(except if numerator is zero in the same time)*

Look at

We comply with the starting conditions :

**Horizontal** :

The straight line

To find easily the limit when x go to

*Limit calculation :*

And

Then :

Do the same reasoning when

Therefore :

**Oblique** :

No oblique asymptote because

To sum up, look at the graph below :

Note :