linear function
I. Constants and variables:
In the process of a change, the amount of numerical change is called variable; A quantity whose value remains constant is called a constant.
Second, the concept of function
Third, the solution of the range of independent variables in the function:
(1) For functions expressed by algebraic expressions, the values of independent variables are all real numbers.
(2) For functions expressed by fractions, the range of independent variables is all real numbers with denominators other than 0.
(3) For functions expressed by radicals, the ranges of independent variables are all real numbers.
For functions with even roots, the range of independent variables is a real number that makes the square root non-negative.
(4) If the analytical formula is synthesized by the above forms, we must first find out the value range of each part, and then find out the common * * * range, which is the value range of the independent variable.
(5) For those related to practical problems, the range of independent variables should make practical problems meaningful.
Definition of function image: Generally speaking, for a function, if each pair of corresponding values of independent variables and functions are taken as the abscissa and ordinate of points respectively, then the graph formed by these points on the coordinate plane is the image of this function.
Fifth, the general steps of drawing function images by tracing point method.
1, list (The values of some independent variables and their corresponding function values are given in the table. )
Note: when listing independent variables, the difference from small to large is the same, and sometimes symmetry is needed.
2. Plot points: (In rectangular coordinate system, the points corresponding to the values in the table are plotted with the values of independent variables as abscissa and corresponding function values as ordinate.
3. Connecting line: (according to the order of abscissa from small to large, connect the traced points with smooth curves).
Summary of knowledge points: There are three representations of functions (1): list method (2) image method (3) analytical method.
Cartesian coordinates/Cartesian coordinates
Plane Cartesian coordinate system: Draw two mutually perpendicular number axes with coincident origin on the plane to form a plane Cartesian coordinate system.
The horizontal axis is called X axis or horizontal axis, the vertical axis is called Y axis or vertical axis, and the intersection of the two coordinate axes is the origin of the plane rectangular coordinate system.
Elements of a plane rectangular coordinate system: ① On the same plane; ② Two axes of numbers are perpendicular to each other; ④ The origin coincides.
Three rules:
① The specified positive direction: the horizontal axis is right, and the vertical axis is oriented in the positive direction.
(2) the provisions of the unit length; Generally speaking, the unit length of the horizontal axis and the vertical axis is the same; In fact, sometimes it can be different, but it must be on the same axis.
③ Quadrant definition: the upper right is the first quadrant, the upper left is the second quadrant, the lower left is the third quadrant, and the lower right is the fourth quadrant.
I believe that the students have mastered the knowledge of plane rectangular coordinate system, and I hope they can all be admitted.
Composition of plane rectangular coordinate system
Two number axes perpendicular to each other on the same plane and having a common origin form a plane rectangular coordinate system, which is called rectangular coordinate system for short. Usually, the two number axes are placed in the horizontal position and the vertical position respectively, and the right and upward directions are the positive directions of the two number axes respectively. The horizontal axis is called X axis or horizontal axis, the vertical axis is called Y axis or vertical axis, and the X axis or Y axis is collectively called coordinate axis, and their common origin O is called the origin of rectangular coordinate system.
Through the explanation and study of the composition knowledge of plane rectangular coordinate system, I hope students can master the above contents well and study hard.
Properties of point coordinates
After the plane rectangular coordinate system is established, the coordinates of any point on the coordinate system plane can be determined. Conversely, for any coordinate, we can determine a point it represents on the coordinate plane.
For any point C on the plane, the intersection point C is perpendicular to the X-axis and Y-axis respectively, and the corresponding points A and B perpendicular to the X-axis and Y-axis are respectively called the abscissa and ordinate of the point C, and the ordered real number pairs (A, B) are called the coordinates of the point C. ..
A point is in different quadrants or coordinate axes, and its coordinates are different.
I hope that the students can master the knowledge of the above coordinate nature, and I believe that the students will achieve excellent results in the exam.
General steps of factorization
If the polynomial has a common factor, first mention the common factor, and then consider the formula method if there is no common factor. If it is a polynomial with four or more terms,
Usually, the group decomposition method is used, and finally the cross multiplication factor is used to decompose the factors. So it can be summarized as "one mention", "two sets", "three groups" and "forty words".
Note: Factorization must be decomposed until each factor can no longer be decomposed, otherwise it is incomplete factorization. If the topic does not clearly indicate the scope of factorization, it should refer to factorization within rational numbers, so the result of factorization must be the product of several algebraic expressions.
I believe the students have mastered the general steps of factorization, and I hope they will do well in the exam.
factoring
Definition of factorization: transforming a polynomial into the product of several algebraic expressions is called factorization of this polynomial.
Factorizing elements: ① The result must be an algebraic expression ② The result must be a product ③ The result is an equation ④.
The relationship between factorization and algebraic expression multiplication: m(a+b+c)
Common factor: The common factor of each term of a polynomial is called the common factor of each term of this polynomial.
Determination of common factor: ① When the coefficient is an integer, take the greatest common factor of each term. The product of the greatest common divisor of the same letter and the lowest power of the same letter is the common factor of this polynomial.
To select a common factor:
① Determine the common factor. ② Determine the quotient formula ③ The common factor formula and the quotient formula are written in the form of product.
Factorizing attention;
(1) Lost letters are not allowed.
(2) It is not allowed to lose the same items. Please check the quantity of items.
③ Change the double brackets into single brackets.
(4) The results are arranged in the order of number, single letter and single polynomial.
⑤ The same factor is written as a power.
⑥ The first minus sign is placed outside the brackets.
⑦ Similar items in brackets are merged.