1. Induction of two compulsory knowledge points in senior one mathematics.
The parity of 1. function (1) If f(x) is an even function, then f (x) = f (-x);
(2) If f(x) is odd function and 0 is in its domain, then f(0)=0 (which can be used to find parameters);
(3) The parity of the judgment function can be defined in equivalent form: f (x) f (-x) = 0 or (f (x) ≠ 0);
(4) If the analytic formula of a given function is complex, it should be simplified first, and then its parity should be judged;
(5) odd function has the same monotonicity in the symmetric monotone interval; Even functions have opposite monotonicity in symmetric monotone interval;
2. Some questions about compound function.
Solution of the domain of (1) composite function: If the domain is known as [a, b], the domain of the composite function f[g(x)] can be solved by the inequality a≤g(x)≤b; If the domain of f[g(x)] is known as [a, b], find the domain of f(x), which is equivalent to x∈[a, b], and find the domain of g(x) (that is, the domain of f(x)); When learning functions, we must pay attention to the principle of domain priority.
(2) The monotonicity of the composite function is determined by "the same increase but different decrease";
3. Function image (or symmetry of equation curve)
(1) Prove the symmetry of the function image, that is, prove that the symmetry point of any point on the image about the symmetry center (symmetry axis) is still on the image;
(2) Prove the symmetry of the image C 1 and C2, that is, prove that the symmetry point of any point on C 1 about the symmetry center (symmetry axis) is still on C2, and vice versa;
(3) curve C 1: f (x, y) = 0, and the equation of symmetry curve C2 about y=x+a(y=-x+a) is f(y-a, x+a)=0 (or f(-y+a,-x+a) =
(4) Curve C 1:f(x, y)=0 The C2 equation of the symmetrical curve about point (a, b) is: f(2a-x, 2b-y) = 0;
(5) If the function y=f(x) is constant to x∈R and f(a+x)=f(a-x), the image of y=f(x) is symmetrical about the straight line x=a, so high school mathematics;
(6) The images of functions y=f(x-a) and y=f(b-x) are symmetrical about the straight line x=;
2. Senior one mathematics compulsory two knowledge points induction
1, parabola is an axisymmetric figure. The symmetry axis is a straight line x =-b/2a.
The intersection of symmetry axis and parabola is the vertex p of parabola.
Especially when b=0, the symmetry axis of the parabola is the Y axis (that is, the straight line x=0).
2, parabola has a vertex p, coordinates are
P(—b/2a，(4ac—b’2)/4a)
-b/2a = 0, p is on the y axis; When δ = b' 2—4ac = 0, P is on the X axis.
3. Quadratic coefficient A determines the opening direction and size of parabola.
When a>0, the parabola opens upwards; A0), the symmetry axis stays on the y axis;
When A and B have different signs (namely ab0), the parabola has two intersections with the X axis.
When δ= b'2—4ac = 0, there are 1 intersections between parabola and X axis.
δ= b ' 2—4ac