Teaching plan of parity of mathematical function in the first volume of senior one of People's Education Press.
First, the teaching objectives
Knowledge and skills
Understand the parity of function and its geometric significance.
Process and method
Use the image and nature of exponential function and monotonicity to solve problems.
Emotional attitudes and values
Experience exponential function is an important function model, which can stimulate students' interest in learning mathematics.
Second, the difficulties in teaching
focus
Parity of Function and Its Geometric Significance
difficulty
Methods and formats for judging the parity of functions.
Third, the teaching process
(A) the introduction of new courses
Take a piece of paper, draw a plane rectangular coordinate system on it, draw a graph that can be used as a function image in the first quadrant, and then answer the corresponding questions as follows:
1 Fold the paper in half with the Y-axis as the crease, draw the trace of graphics in the first quadrant (that is, the second quadrant) on the back of the paper, then unfold the paper and observe the graphics in the coordinate system;
Question: If the graph of the first quadrant and the second quadrant is regarded as a whole, can this graph be regarded as an image of a function y=f(x)? If yes, please tell me what special properties this image has. What is the special relationship between the coordinates of the corresponding points on the function image?
Answer: (1) can be the image of a function y=f(x), and its image is symmetrical about y axis;
(2) If the point (x, f(x)) is on the function image, the corresponding points (-x, f(x)) are also on the function image, that is, the points with opposite abscissas on the function image, their ordinate must be equal.
(B) the new curriculum teaching
Definition of parity of 1. function
The function of image symmetry about Y axis in operation 1 is even function, and the function of image symmetry about origin in operation 2 is odd function.
(1) even function
Generally speaking, f (-x) = f(x) exists for any x in the domain of function f(x), so f (x) is called even function.
(Student activity): Imitate the definition of even function and give the definition of odd function.
(2) odd function.
Generally speaking, F (-X) = f(x) exists for any X in the domain of function f(x), so F (X) is called odd function.
note:
The odd function of 1 function or even-numbered function is called the parity of function, and the parity of function is the global property of function.
According to the definition of function parity, a necessary condition of function parity is that -x must also be an independent variable in the definition domain for any x in the definition domain (that is, the definition domain is symmetrical about the origin).
2. Features of images with parity function
The image of even function is symmetrical about y axis;
Odd function's image is symmetrical about the origin.
3. Typical examples
(1) Judging the parity of a function
Example 1. (Textbook P36, Example 3) Use the definition of function parity to illustrate the parity of four functions in two observations and reflections. (This example is discussed by students, and the teachers and students summarize the specific methods and steps. )
Solution: (omitted)
Summary: Format steps for judging the parity of a function according to the definition:
1 First, determine the definition domain of the function and judge whether its definition domain is symmetrical about the origin;
2 determine the relationship between f(-x) and f(x);
3. Draw corresponding conclusions:
If f(-x) = f(x) or f(-x)-f(x) = 0, then f(x) is an even function;
If f(-x) =-f(x) or f(-x)+f(x) = 0, then f(x) is odd function.
(3) Consolidate and improve
1. textbook P46 exercise 1.3 B group each 1 question.
Solution: (omitted)
Note: A necessary condition for a function to have parity is that its domain is symmetric about the origin, so to judge the parity of a function, we must first judge whether the domain of the function is symmetric about the origin, and if not, we can conclude that the function is a parity function.
2. Complete the mapping of the function by using the parity of the function.
(Textbook P4 1 Thinking Questions)
Law:
The image of even function is symmetrical about y axis;
Odd function's image is symmetrical about the origin.
Note: this can also be used as a basis for judging the parity of functions.
(4) Summarize the homework
This section mainly studies the parity of functions. There are usually two methods to judge the parity of a function, namely, definition method and mirror method. When judging the parity of a function by definition, we must first judge whether the domain of the function is symmetrical about the origin. The comprehensive application of monotonicity and parity is a difficult point in this section, which requires students to fully understand monotonicity and parity in combination with the image of functions.
Textbook P46 Exercise1.3 (Group A) Question 9 and 10, Group B Question 2.
Fourth, blackboard design.
Parity of function
1. even function: generally speaking, for any x in the definition domain of function f(x), there is f(-x)=f(x), so f(x) is called even function.
Odd function: Generally speaking, for any X in the domain of function f(x), there is f(-x)=f(x), so f(x) is called odd function.
Third, the law:
The image of even function is symmetrical about y axis;
Odd function's image is symmetrical about the origin.
People who have seen the parity teaching plan of mathematical function in the first volume of senior one also read:
1. Eight Grade One Mathematics Inequality Teaching Plan
2. The application practice of the first volume of the eighth grade mathematics.
3. The first volume of the eighth grade mathematics exercises the group of one yuan and one time inequalities.
4. Reflections on the teaching of first-order functions and first-order inequalities in junior two mathematics.
5. Tutoring materials for second-year mathematics: one-dimensional linear inequality group