The three expressions of function are function expression, graphic expression and program code expression.
1, function expression
Use mathematical symbols and formulas to express the definition and properties of functions. For example, a simple quadratic function can be expressed as f (x) = ax 2+bx+c, where a, b and c are constants and x is an independent variable. This expression directly gives the definition of function and the relationship between variables, and is widely used in mathematics.
2、? diagrammatic presentation
Functions can also be represented graphically. By drawing the image of the function in the coordinate system, the properties and characteristics of the function can be displayed intuitively. Graphical representation is suitable for analyzing the overall form and changing trend of functions, such as finding the maximum value, minimum value and zero point of functions. Common examples are parabola, sine curve and so on.
3, the program code expression
With the development of computers, functions can also be expressed by program codes. Programming languages provide definitions and calling methods of various functions, which can realize various complex functions. The expression of program code is more flexible and concrete, and various functions can be realized by writing algorithms and logic, such as sorting, searching, image processing and so on.
Importance and application of function expression
Importance of 1. function expression
Function expressions provide an accurate and clear way to define functions, and the properties and changing laws of functions can be accurately described by mathematical symbols and formulas.
Function expression is the basis of mathematical and scientific research, and many important mathematical theories and theorems are based on the research and analysis of function expression.
Function expressions can be used to model and solve practical problems. According to the requirements of the problem, we can construct corresponding function expressions to describe and calculate, and then get the solution of the problem.
2. The application of function expression
In physics, functional expressions are used to describe the relationships between various physical quantities, such as the equations of motion in Newtonian mechanics and Maxwell equations in electromagnetism.
In economics, function expressions are used to describe the relationship between supply and demand, production function, cost function and so on. To provide a basis for economists to study economic phenomena and formulate economic policies.
In engineering, function expressions are used to analyze and design control systems, signal processing and circuit design. To help engineers realize complex functions and optimize performance.
In computer science, function expressions are used to define and call functions in programming languages, which provides a method of modularization and code reuse, making programs more readable and easy to maintain.