Common conclusions of function symmetry

Odd function, even function and periodic function are the common conclusions of function symmetry.

1, the property of odd function: If the function f(x) is odd function, there exists f(-x)=-f(x) for any x in the definition domain, that is, the image of odd function is symmetrical about the origin. This property shows that odd function's image is symmetrical on both sides of the origin.

2. Properties of even function: If the function f(x) is an even function, there is f(-x)=f(x) for any x in the definition domain, that is, the image of even function is symmetric about y axis. This property shows that the image of even function is symmetrical on both sides of y axis.

3. Properties of periodic function: If the function f(x) is a periodic function, there exists a positive integer t, so that for any x in the definition domain, there exists f(x+T)=f(x). This property shows that the image of periodic function presents periodic symmetry on the X axis. Common periodic functions include sine function and cosine function.

Application of functions:

1. Scientific calculation: Functions can be used for various problems in scientific calculation, such as solving equations, calculating probabilities, statistical data, etc. Through the operation of the function, the calculation result can be obtained more efficiently, and the function can make the calculation process more concise and easy to understand.

2. Data analysis: In the era of big data, the amount of data is increasing, and how to extract useful information from massive data becomes the key. Functions play an important role in data analysis. Linear regression, logistic regression, support vector machine and other machine learning algorithms all involve the use of functions. Using function to fit and predict data can get more accurate results, and function can make data processing more efficient and easy to operate.

3. Financial field: Functions are widely used in the financial field. For example, portfolio theory, we need to calculate the price and yield of assets, which all need functions. In addition, functions also play an important role in risk management, quantitative finance and other fields. Through the operation of the function, more accurate forecasting and pricing results can be obtained, and the function can make the financial calculation process more concise and easy to understand.