Piecewise function is a kind of compound function, which consists of several sub-functions, each of which has its own domain and corresponding rules. The definition domain of piecewise function is the union of the definition domain of each subfunction, while the value domain is the union or intersection of the domain of each subfunction. In piecewise function, each sub-function is defined according to different independent variable values, so the expressions and corresponding rules of piecewise function will be different in different independent variable values.

Although the piecewise function seems to be composed of several functions, it is actually a single function, but different expressions and corresponding rules are adopted according to the range of independent variables. So the piecewise function is a single function, not several functions.

Matters needing attention in learning mathematics:

1. Understand and master basic concepts: Mathematics is a subject based on various basic concepts. When learning new mathematical concepts, make sure to understand their definitions and meanings, and try to describe them in your own language. Understanding basic concepts can not only help you better understand complex concepts and formulas, but also improve your problem-solving ability.

2, a lot of practice: Mathematics is a subject that needs a lot of practice. Through repeated practice, you can gradually improve your calculation ability and problem-solving ability. In practice, we should pay attention to quality rather than quantity, and try to understand the thinking of solving problems, not just to get answers.

3. Cultivate problem-solving ability: The goal of learning mathematics is not only to solve mathematical problems in textbooks or test papers, but more importantly, to apply mathematics in real life. Cultivating your ability to solve practical problems and connecting mathematics with daily life will make your mathematics learning more interesting and practical.

4. Use and rely on mathematical tools: Modern science and technology provide many useful tools for learning mathematics, such as calculators, online resources and mathematical software. Proper use of these tools can help you learn mathematics more efficiently, especially when you are doing complex calculations and solving complex problems.