Proportional function and its properties 1. Generally, the function in the form of y=kx(k is constant, k≠0) is called proportional function, where k is called proportional coefficient.
Note: the general form of the proportional function is y=kx, and k is not zero.
(1)k is not zero;
(2) the x index is1;
(3)b takes zero.
2. When k>0, the straight line y=kx rises from left to right through three or one quadrant, that is, Y also increases with the increase of X;
3. when k
(1) analytical formula: y=kx(k is a constant, k≠0)
(2) Necessary points: (0,0), (1, k)
(3) Trend: k>0, the image passes through the first and third quadrants; K<0, the image passes through two or four quadrants.
(4) Increase or decrease: k>0 and Y increase with the increase of X; K<0, y decreases with the increase of x.
(5) Inclination: The greater the |k|, the closer it is to the Y axis; The smaller the |k|, the closer it is to the X axis.
Linear function and its properties 1. Generally speaking, if the shape is y=kx+b(k and b are constants, 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, and k is not zero.
(1)k is not zero;
(2) the 2)0x index is1;
(3)b is an arbitrary real number.
2. The image with linear function y=kx+b is a straight line passing through two points (0, b) and (-k/b, 0). We call it a straight line y=kx+b, which can be regarded as a straight line y=kx translating |b| unit lengths.
(1) analytical formula: y = kx+b;
(2) Necessary points: (0, b) and (-k/b, 0);
(3) Trends:
(4)k & gt； 0, the image passes through the first and third quadrants; K<0, the image passes through the second and fourth quadrants;
(5)b & gt； 0, the image passes through the first and second quadrants; B<0, the image passes through the third and fourth quadrants.
Quadratic function 1, definition: Generally speaking, there is the following relationship between independent variable x and dependent variable y: y = ax 2+bx+c (a, b and c are constants, a≠0, and a determines the opening direction of the function).
2. Three expressions of quadratic function
(1) general formula: y = ax 2+bx+c (a, b, c are constants, a≠0).
(2) Vertex: y = a(x-h)2+k[ vertex P(h, k) of parabola]
(3) Intersection point: y=a(x-x? )(x-x？ ) [only when it is related to the x axis A(x? , 0) and B(x? 0) parabola]
The property of parabola is 1, and parabola is an axisymmetric figure. The symmetry axis is a straight line x=-b/2a.
The only intersection of the symmetry axis and the parabola is the vertex p of the parabola. Especially when b=0, the symmetry axis of the parabola is the Y axis (that is, the straight line x=0).
2. The parabola has a vertex p, whose coordinates are: P(-b/2a, (4ac-b 2)/4a) When -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 upward; When a < 0, the parabola opens downward. The larger the |a|, the smaller the opening of the parabola.
These are the knowledge points of functions that I have compiled, and I hope they can help you.