1. Periodicity of function

　　In high school, we learned about the periodicity of functions , including periodic functions, minimum positive periods, characteristics of periodic functions , etc. The concept of function periodicity learned in college is consistent with what was learned in high school.

　　Definition: Let the domain of function be , if there is a real number that is not zero , such that , there is , and

Then is called a periodic function, is the period of .

　　For example, functions and are both periodic functions with as the period; function is a periodic function with as the period.

　　2. Characteristics of periodic functions

　　If  the graph of a periodic function with period in one period is translated to the left or right by an integer multiple of the period, it will coincide with other parts of the periodic function.

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　　Usually the period of a periodic function refers to its minimum positive period. But not every periodic function has a minimum positive period.

　　3. Regarding the judgment of the periodicity of a function, it is generally proved by using the definition and the operation properties of the periodic function. The key to the proof is to construct a suitable starting from the definition , so that

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　　The application of periodic functions is widespread because many phenomena we study in science and engineering technology show obvious periodic characteristics. For example, household voltages and currents are periodic, and the electromagnetic fields in microwave ovens used to heat food are periodic, seasons and climate are cyclical, moon phases and planetary movements are cyclical, etc.