2. In a set, Cu(A∩B)=(CuA)U(CuB), and the complement of intersection is equal to the sum of complement. Cu(AUB)=(CuA)∩(CuB), and the complement of the union is equal to the complement.
3、ax2+bx+c & lt； The solution set of 0 is x (0
+c & gt； The solution set of 0 is x, and the solution set of cx2+bx+a > 0 is > x or x; X or x 0) move y = f (x) to the left or right by one unit;
(2) vertical translation: y = f (x) b (b >; 0) image, which can be obtained by moving y=f(x) up or down by b units;
(3) Symmetry: If F (X+M) = F (X-M) exists for all x in the defined domain, then the image of y=f(x) is symmetrical about the straight line x=m; Y=f(x) The symmetric function about (a, b) is y! =2b—f(2a—x)。
(4) and Nbsp, learning plan; Folding: ① Y = | f (x) | is an image with the X axis as the symmetry axis, and the part where y=f(x) is located below the X axis is folded above the X axis. ② y = f (| x |) is an image obtained by folding the image of y=f(x) on the left side of the y axis to the right side of the y axis.
(5) Relevant conclusions: ① If f (a+x) = f (b-x) is true when x is all real numbers, then the image of y=f(x) is about
X= symmetry. ② The images of function y = f (a+x) and function y = f (b-x) are symmetrical about the straight line x=.
15, arithmetic progression, an = a1+(n-1) d = am+(n-m) d; sn=n=na 1+
16, if n+m = p+q, then am+an = AP+AQ; Sk, s2k-k and s3k-2k form a arithmetic progression with a tolerance of k2d. Ann is arithmetic progression, if AP = Q and AQ = P, then AP+Q = 0；; If sp = q and sq = p, then sp+q =-(p+q); If sk, sn, sn-k and sn = (sk+sn+sn-k)/2k are known; If an is arithmetic progression, let the sum of the first n terms be Sn = AN2+BN (note: there is no constant term), and solve A and B with the idea of equation. In arithmetic progression, if the item with the foot code arithmetic progression is taken out to form a series, the new series is still arithmetic progression.
17, geometric series, an=a 1? qn- 1=am？ Qn-m, if n+m = p+q, am? an=ap？ AQ； sn=na 1(q= 1)，
sn=，(q≠ 1)； If q≠ 1, then there is =q, if q ≠- 1, = q;
SK, S2K-K and S3K-2K are also geometric series. A 1+A2+A3, A2+A3+A4, A3+A4+A5 also form geometric series. In geometric progression, if the item with the foot code arithmetic progression is taken out to form a series, the new series is still geometric progression. Crack formula:
=—,=? (—), recurrence forms of commonly used series: superposition, superposition, multiplication,
18, arc length formula: l=|α|? R .s fans =? lr=？ |α|r2=？ ; When the perimeter of the sector is constant (L),
Its area is, and its central angle is 2 radians.
19、Sina(α+β)= sinαcosβ+cosαsinβ； Sina(α—β)= sinαcosβ—cosαsinβ；
cos(α+β)= cosαcosβ—sinαsinβ； cos(α—β)=cosαcosβ+sinαsinβ
two
Content intersection and complement set, and power exponential pair function. Parity and increase and decrease are the most obvious observation images.
When the compound function appears, the law of property multiplication is distinguished. To prove it in detail, we must grasp the definition.
Exponential function and logarithmic function, junior high school learning methods, are inverse functions. Cardinality is not a positive number of 1, and 1 increases or decreases on both sides.
The domain of the function is easy to find. Denominator cannot be equal to 0, even roots must be non-negative, and zero and negative numbers have no logarithm;
The tangent function angle is not straight, and the cotangent function angle is uneven; The real number sets of other functions have intersection in many cases.
Two mutually inverse function have that same monotone property; The images are symmetrical with Y=X as the symmetry axis;
Solve the very regular inverse solution of substitution domain; The domain of inverse function, the domain of original function.
The nature of power function is easy to remember, and the index reduces the score; Keywords exponential function, odd mother and odd son odd function,
Even function with odd mother and even son, even mother non-parity function; In the first quadrant of the image, the function is increased or decreased to see the positive and negative.
A function in the form of y = k/x (where k is a constant and k≠0) is called an inverse proportional function.
The range of the independent variable x is all real numbers that are not equal to 0.
Inverse proportional function image properties:
The image of the inverse proportional function is a hyperbola.
Since the inverse proportional function belongs to odd function, let f(-x)=-f(x), and the image is symmetrical about the origin.
In addition, from the analytical formula of the inverse proportional function, it can be concluded that any point on the inverse proportional function image is perpendicular to the two coordinate axes. In high school geography, the rectangular area surrounded by this point, two vertical feet and the origin is a constant value, right? k？ .
As shown in the figure, the function images when k is positive and negative (2 and -2) are given above.
When K>0, the inverse proportional function image passes through one or three quadrants, it is a decreasing function.
When k < 0, the inverse proportional function image passes through two or four quadrants, which is increasing function.
The inverse proportional function image can only move towards the coordinate axis infinitely, and cannot intersect with the coordinate axis.
Knowledge points:
1. Any point on the inverse proportional function image is a vertical line segment of two coordinate axes, and the area of the rectangle surrounded by these two vertical line segments and the coordinate axes is k.
2. For hyperbola y=k/x, if you add or subtract any real number on the denominator (that is, y = k/(x m) m is a constant), it is equivalent to translating the hyperbola image to the left or right by one unit. (When adding a number, move to the left, and when subtracting a number, move to the right)