Why is #y=1/x# a continuous function?
This function has a point of discontinuity at
So this function is NOT continuous as it has asymptotes along the lines
We first need to determine the domain of
Hence, the domain of
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
On the other hand, the function