# Why is #y=1/x# a continuous function?

##### 4 Answers

#### Explanation:

This function has a point of discontinuity at

Similarly,

So this function is NOT continuous as it has asymptotes along the lines

#### Explanation:

We first need to determine the domain of

Hence, the domain of

Now,

Since

See below.

#### Explanation:

You seem to be getting conflicting information on this. One of the reasons is because continuity is generally referring to a given point or interval. The function is said to be discontinuous at a point if the limit at that point dosen't exist. So for a function to be continuous over the domain, the limit of any point in the domain must exist. For the function

The domain under consideration determines the answer here. The function

#### Explanation:

The function **not** continuous on

On the other hand, the function **is** removable. The fact that