Junior 2 Mathematics Inverse proportional function Please answer in detail, thank you 19 15 9 0

1.Suppose y1=k x, y2=a(x-2) then, y=k x-a(x-2) when x=3, y=5, when x=1, y=-1:

k 3-a=5, k + a = -1 yields: k = 3, a = -4y = 3 x + 4 (x-2).

2.The two functions intersect at a point, and the point a is on the two functions: m 3 = 3k + b 1 = m -2

1=-2k+b③

Solution: m=2, k=1 3, b=-1 3: y=2 x, y=1 3x-1 3

Let y=k1 x-k2(x-2), which is substituted by y=3, y=5, x=1, and y=-1.

k1=3/2,k2=1/2

So y=3 2x-(x-2) 2

m=-1*-2=2

From -1=2k+b and 2 3=3k+b, k=5 3, b=-13 3 is obtained

Let y1=a x y2=b(x-2).

Then y=y1-y2=a x-bx-2b

y=a 3-3b-2b=a 3-b=5x=1 when x=3 y=a-b-2b=a-3b=1

Solve the binary linear equation a=-7 b=-8 3

So y=-7 x+8x 3+16 3

Solution: Let the inverse proportional function be y=-k x The condition of the problem is that the triangle AOD congruent triangle EOD So ao=0e=5 OC=20 3 OB=25 3 The perpendicular line of OC is crossed by the point E and intersects OC at point F, then the RT triangle OEF is similar to the RT triangle OEC, and their corresponding line segments correspond to proportional columns. So.

OE:ob=ef:bc so EF=OE*BC ob EF= 5*5 (25 3)=3

of：oc=ef：bc of*bc=oc*ef of=oc*ef/bc= 20/3*3/5=4

So the coordinates of point e are (- 4,3) and substituting y=-k x gives k=12, so y=-12 x

How much is the abscissa of point b?

Let y=-ax-1 power, and the coordinates of point e are obtained from the coordinates of point b and the similarity triangle theorem.

When x -3, the primary function is greater than the inverse proportional function, and when x 2, the primary function is less than the inverse proportional function, as you can see in the diagram.

When x is less than minus 3 and x is less than 0 and greater than 2, the primary function is greater than the inverse proportional function. When x is greater than 2 and x is less than 0 and less than minus 3, the primary function is less than the inverse proportional function. Ask me if there is anything I don't understand.

1).Since the primary function y=2x-1 image passes through the point (k,5), so 2k-1=5, so k=3, so the inverse proportional function of the derivation of the analytic segment is y=3 x

2).Point A is on the image of the above two functions at the same time, so the abscissa of point A is the solution of Equation 3 x=2x-1, and the solution of Equation 3 x=2x-1 gives x=-1 or x=3 2, because point A is in the first quadrant, so the dust is old x=3 2, so Y=2, so the coordinates of point A are (3 2,2).

Not necessarily. The proportional function y=1 x, the primary function y=a*x+b, if the figures intersect, the two equations are conjoined to obtain.

a*x 2+b*x-1=0, when b=0, then obviously x obtains the value of opposite numbers, and then by y=1 x, the solved intersection coordinates must be symmetrical about the origin;

When b is not equal to 0, the two values of a*x 2+b*x-1=0 are added to -b a, which cannot be 0, that is to say, the two values cannot be opposite to each other, and the coordinates of the intersection are no longer symmetrical about the origin.

Naturally, the conjecture is wrong.

Because a primary function is not the same as a proportional function.

To put it simply, the proportional function is a special case of the primary function (y=kx+b, b=0), so how to change from a proportional function to a primary function?

In fact, as long as the proportional function is translated b units along the y-axis, any primary function can be obtained.

The intersection of the proportional and inverse proportional functions is symmetrical with respect to the origin.

The primary function and the inverse proportional function after translation will be symmetrical with respect to the point (0,b).

Therefore, the correct coordinate relationship is: let one of the intersection coordinates be (x,y) and the other intersection coordinate (-x,2b-y).

10•600=6000

A: It takes at least 15 months for all the money to be paid in full.

The first delivery is not to be known.

Inverse proportional function, what you are learning now is a relatively simple inverse proportional function, that is, y=1 x, such an inverse proportional function, basically you can understand such an inverse proportional function, and you will learn what you need to master in the three years of junior high school. What is the asymptote, as shown in the figure, the x, y axis is the asymptote, the asymptote is infinitely close, but the line that cannot be touched, is the number that cannot be obtained, how to understand, take this as an example:

y=1 x, the denominator is not zero, so x is not 0, the function can also be changed to x=1 y, so y is not 0, in summary, x, y can not be taken to 0, according to the image, it is drawn as gradually approaching but can not be taken, that is, the asymptote line. That's pretty much the simplest explanation.

As long as junior high school students learn how to draw a picture, they can choose 3 or 4 values on each side and draw a picture.

The image of the inverse proportional function is hyperbola, and the distance between the points on the curve and the x-axis is getting closer and closer to 0, then the x-axis is the asymptote of the curve.

The function image is about the same as a primary function.

For example, y=1 x

1. List. x -3 -2 -1 0 1 2 3y -1 3 -1 -1 -1 none 1 1 2 1 32, in the plane Cartesian coordinate system, trace the point with (x,y) as the coordinates (-3,-1 3), (2,-1 2), (1,-1) ......3. Connect with smooth curves.

Attention: Because there is no value for y when x=0, this curve is divided into two segments, which is called hyperbolic hyperbola and the coordinate axis do not intersect.

It's simple, the list is dotted and connected.

5xy=10000

xy=2000

y=2000/x

Since, in a cuboid, the length is wide, so the range of y is:

y>5 is 2000 x>5

2000>5x

x<400

Therefore, the value range of x is: 0