1. Definition of continuity: If the function f(x) is defined in x0 and the limit is equal to the function value, then the function is continuous in x0.

2. Sufficient condition: If the function f(x) is differentiable or differentiable at x0 (or stronger condition), then the function is continuous at x0.

3. Necessary condition: If the function f(x) is not defined at x0, or has no limit, or the limit is not equal to the function value, it is discontinuous at x0.

4, observe the image (this is not rigorous, only for intuitive judgment)

5. Remember the properties of some basic elementary functions. Most elementary functions are continuous in the domain of definition.

6. Properties of continuous functions: The addition, subtraction, multiplication and composite functions of continuous functions are all continuous.