High School Mathematics Knowledge Sharing Keywords: High School Mathematics, Function Concept, Definition, Properties, Applications.
I. Introduction. Functions are an important concept in mathematics and one of the core contents of high school mathematics. It describes the dependencies between two quantities in mathematics, providing us with a valid mathematical model. This article will provide an in-depth analysis of the concept of functions in high school mathematics to help readers better understand and master the basic knowledge of functions.
2. Definition and representation of functions.
Definition of a function: A function is a special correspondence that describes a definite correspondence between two sets of non-empty numbers. Let a and b be two non-empty sets of numbers, and if, according to some definite correspondence f, there is a uniquely definite number f(x) corresponding to any number x in set a, then f:a b is said to be a function from set a to set b.
Representation of functions: Functions can be represented in three ways: analytical, graphic, and **. Among them, an analytic expression is a method of expressing a function with a mathematical formula, such as f(x) = x 2;An image is a method of representing a function by points on a planar Cartesian coordinate system;** is a method of representing a function by listing the values of some independent variables and the corresponding function values.
3. The nature of the function.
Monotonicity of a function: The monotonicity of a function describes the tendency of the value of a function to change with the change of the independent variable. If, within an interval, the value of a function increases (or decreases) as the independent variable increases, then we say that the function is monotonically increasing (or decreasing) within that interval.
Parity of a function: Parity of a function describes the symmetry of an image of a function with respect to the origin or y-axis. If there is f(-x) = -f(x) for any x in the field where the function f(x) is defined, then we say that the function is odd;If there is f(-x) = f(x) for any x in the domain where the function f(x) is defined, then we say that the function is even.
Periodicity of a function: The periodicity of a function describes the repeatability of an image of a function. If there is a positive number t such that for any x in the defined domain of the function f(x) there is f(x + t) = f(x), then we say that the function is a periodic function and t is the period of this function.
Fourth, the application of functions.
As an important concept in mathematics, functions have a wide range of applications in practical life. For example, in economics, we can use functions to describe market supply and demand;In physics, we can use functions to describe the state of motion of an object;In engineering, we can use functions to describe mathematical models of various engineering problems. Therefore, mastering the basic knowledge of functions is of great significance for us to understand these practical problems.
5. Summary and outlook.
This article provides an in-depth analysis of the concept of functions in high school mathematics to help readers better understand and master the basic knowledge of functions. By learning and mastering the definition, representation, properties and applications of functions, readers can have a deeper understanding of the basic concepts and operation rules in mathematics, and improve their logical thinking ability and mathematical literacy. At the same time, we should also be aware of the important position and role of functions in mathematics, and constantly explore their application prospects and development space in various fields.