1. Understand the basic concept of function: First of all, you need to know what a function is, what its definition is, and what its basic properties are. These basic knowledge can be learned by reading textbooks or attending classes.
2. Learn the image and properties of the function: After learning the basic concepts of the function, you need to learn how to draw the image of the function and understand various properties of the function, such as increase and decrease, parity and so on. You can deepen your understanding of the nature of functions by doing exercises or searching online resources.
3. Master the operation and transformation of functions: learn four operations of functions, compound operations and some common function transformations, such as translation and expansion. These operations and transformations are important contents in function learning and need more practice to master them skillfully.
4. Understand elementary function: Elementary function is one of the commonly used function types in mathematics, and it is necessary to understand its definition, image and properties. You can learn by reading textbooks or looking up relevant materials.
5. Cultivate mathematical thinking: Learning mathematical functions is not only to master some basic knowledge and skills of functions, but also to cultivate mathematical thinking. By solving practical problems and exploring the nature and laws of functions, you can gradually improve your mathematical thinking ability.
Characteristics of mathematical functions
1, correspondence: the core of a function is correspondence, that is, given an independent variable X, there is a unique dependent variable Y corresponding to it. This correspondence can be a direct arithmetic operation or a more complicated mathematical relationship.
2. Determinism: For each independent variable X, there is a unique dependent variable Y corresponding to it, and this correspondence is deterministic and has no randomness. Continuity: at every point in the function definition domain, the value of the dependent variable y is certain and continuous. This means that the function has no discontinuity in the domain.
3. Monotonicity: Monotonicity of a function means that the dependent variable Y increases (or decreases) with the increase (or decrease) of the independent variable X in a certain interval. Boundedness: the range of the function is bounded, that is, the range of the dependent variable y is limited.
4. Parity: If the image of a function is symmetrical about the origin, then this function is odd function; If the image of a function is symmetric about y, then the function is even. Periodicity: Some functions are periodic, that is, their values will appear repeatedly according to a certain period. For example, sine function and cosine function are both periodic functions.