# How do you find the points of continuity and the points of discontinuity for a function?

A simple statement can be made as follows:

The points of discontinuity are that where a function does not exist or it is undefined.

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To find the points of continuity for a function, we need to check three conditions:

- The function must be defined at that point.
- The limit of the function as x approaches that point must exist.
- The value of the function at that point must be equal to the limit.

To find the points of discontinuity for a function, we need to identify any points where one or more of the above conditions are not met. Discontinuities can be classified into three types:

- Removable discontinuity: The limit exists, but the value of the function at that point is different from the limit.
- Jump discontinuity: The limit exists, but the value of the function "jumps" from one side of the point to the other.
- Essential discontinuity: The limit does not exist at that point.

By analyzing the function and applying these conditions, we can determine the points of continuity and discontinuity.

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