Foreword
Function Concept:
The concept has two functions, one for the definition of junior high school, called traditional definition, the other is the definition of high school, known as the modern definition.
Traditional definition : a process of change provided there are two variables \ (X \) , \ (Y \) , if for \ (X \) each determined value within a certain range, \ (Y \) are there are uniquely determined and it corresponds to the value, then called \ (y \) is \ (x \) function, \ (x \) is called the independent variable. We will argument \ (X \) domain, and a set of values is called argument function \ (X \) corresponding to \ (Y \) values is called the function value, the function value is called a set of range function.
Modern definitions : Let \ (A \) , \ (B \) are non-empty set of numbers, \ (F: X → Y \) is the \ (A \) to \ (B \) corresponding rule, then from \ (a \) to \ (B \) mapping \ (f: a → B \ ) is called a function, referred to as \ (Y = F (X) \) , where \ (x∈A \) , \ (y∈B \) , the original set as \ (a \) function called \ (f (x) \) of the domain, as set \ (C \) function called \ (f (x) \) of the range, obviously there \ (C \ subseteq B \) .
- Understanding of the concept of function
Two definitions of the nature of the function is the same, only different narrative starting point the concept of the traditional definition is from the viewpoint of change in motion, but the modern definition is from the collection, view maps departure. Thus, it is difficult to learn the substance is a function of a particular number of non-null mapping A to B from a non-empty set number.
- Why do such an arrangement?
Perspective on teaching practice in high school, high school students receive map the abstract mathematical concepts are very difficult, not to mention the junior high school students, junior high and therefore the general arrangements for the traditional definitions to describe the function, change the view from sports-defined functions, to facilitate students to understand and accept; with the increase of awareness of students, experience increases, the contact function increases, portray the traditional definition of the function definition with increasingly hard to explain the concept of functions, such as Dealey Cray function \ ( f (x) = \ left \ {\ begin {array} {l} {1, x \ in Q} \\ {0, x \ not \ in Q,} \ end {array} \ right. \) she essentially corresponding to a reflected, rather than changes in the movement process. Therefore, the need to adjust the definition of the function;
It also needs to be noted that the use of modern function is defined to characterize the function, she also needs to be backward compatible with the traditional definition. This is met. Therefore, using the first definition to the high school, and then define the mapping based on the concept corresponding to the last-defined function to map is based.
The concept of angle
Junior Definition: [statically defined] by a radiation pattern consisting of two common endpoint become angular. Thereby defining a readily appreciate that characterize the maximum angle range \ (\ Theta \ in [0 ^ {\ CIRC, 360 ^ {\ CIRC}] \) .
High definition: [Dynamic Definition]