The method of determining the domain of function
When the relation (1) is an algebraic expression, the function domain is all real numbers;
(2) When the relation contains a fraction, the denominator of the fraction is not equal to zero;
(3) When the relation contains quadratic roots, the number of square roots is greater than or equal to zero;
(4) When there is a formula with zero exponent in the relationship, the cardinality is not equal to zero;
(5) In practical problems, the function domain should be consistent with the actual situation in order to make it meaningful.
General steps of determining resolution function by undetermined coefficient method
(1) Write a functional relationship of undetermined coefficients according to known conditions;
(2) Substitute several pairs of values of X and Y or the coordinates of several points on the image into the above functional relationship to obtain an equation with undetermined coefficients as unknowns.
(3) solving the equation to obtain the value of the unknown coefficient;
(4) Substituting the obtained undetermined coefficient into the obtained function relation to obtain the analytical expression of the obtained function. Definition of linear function
Linear functions, also known as linear functions, can be represented by straight lines on the x and y axes. When the value of one variable in a linear function is determined, the value of another variable can be determined by a linear equation.
Representation method of function
List method: it is clear at a glance and easy to use, but the corresponding values listed are limited, so it is not easy to see the corresponding law between independent variables and functions.
Analytical formula method: simple and clear, it can accurately reflect the dependence between independent variables and functions in the whole process of change, but the functional relationship in some practical problems can not be expressed by analytical formula.
Image method: the image is intuitive, but it can only approximately express the functional relationship between two variables.
Natural linear function
Generally speaking, if the shape is y=kx+b(k, b is constant, k≠0), then y is called a linear function of X. When b=0, y=kx+b means y=kx, so the proportional function is a special linear function.
Note: the general form of linear function is y=kx+b(k is not 0).
a)。 K is not 0.
B) the index. X is 1.
c)。 Take any real number.
The image with linear function y=kx+b is a straight line passing through two points (0, b) and (-b/k, 0). We call it a straight line y=kx+b, which can be regarded as a straight line y=kx translation |b| unit length. (When b>0, translate upward; B<0, move down.
Trigonometric function relation
Reciprocal relationship
tanα cotα= 1
sinα cscα= 1
cosα secα= 1
Relationship of quotient
sinα/cosα=tanα=secα/cscα
cosα/sinα=cotα=cscα/secα
Square relation
sin^2(α)+cos^2(α)= 1
1+tan^2(α)=sec^2(α)
1+cot^2(α)=csc^2(α)
Hexagon memory method of equilateral trigonometric function relationship
The structure is "winding, cutting and cutting; Zuo Zheng, the right remainder and the regular hexagon of the middle 1 "are models.
Reciprocal relationship
The two functions on the diagonal are reciprocal;
Quotient relation
The function value of any vertex of a hexagon is equal to the product of the function values of two adjacent vertices. (It is mainly the product of trigonometric function values at both ends of two dotted lines, and this relationship also exists in the following four articles. )。 From this, the quotient relation can be obtained.
Square relation
In a triangle with hatched lines, the sum of squares of trigonometric function values on the top two vertices is equal to the square of trigonometric function values on the bottom vertex.