Mathematics in the second year of junior high school, inverse proportional functions. Help

1) Because the ordinate of p is 6, it is on y=12 x, so.

6=12/x,x=2

So, the coordinates of point p are (2,6), which is again on y=kx-4.

So, 6 = 2k-4

k=5 Therefore, the analytic formula of the primary function is y=5x-42) is conjoined by y=12 x and y=5x-4, and the coordinates of the q point are obtained.

If the coordinates of the intersection of the straight line pq and the x-axis are m(4 5,0), then the area of the triangle POQ = the area of the triangle POM + the area of the triangle QOM = 6*(4 5)*(1 2)+10*(4 5)*(1 2)=32 5

1, because the ordinate of p is 6, so 6=12 x, so, x=2 The coordinates of point p are (2,6) because y=kx-4, the coordinates of point p are brought in as 6=2k-4, so k=5, so the analysis of the primary function is shown as y=5x-4

2, y=5x-4 and y=12 x intersection q, because y=y, so 5x=12 x, simplified to (5x+6)(x-2)=0, so x is -6 5 or 2, so the coordinates of q point are (-6 5, -10), the intersection of the primary function and x is (4 5, 0) so the triangle pqo area is 4 5*2 2+4 5*10 2=

Since the inverse proportional function has an intersection point with the primary function, the analytic formula of the primary function is y 12x

2。Since p has an ordinate of 6, then op 6 because of k 12, then the abscissa of p point is 2So the coordinates of point q are (2,6), then s 8 12 (self-counting).

The upstairs approach should be wrong.

The landlord's primary function should be y=kx+4.

The first question: y=x+4

The second question: the area should be 12

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.

Combining the hyperbola and the straight line AB to calculate the intersection points, which are p(1 4,3 4) and q(3 4,1 4), respectively, proves that pb=qa, and because ob=oa, angle b=angle a, so proof 1 can be obtained

ac=a, angle a=45°, ad=dc=two-a, oa=1, ab=two-part root, according to the similarity of the triangle bed and boa, booe=ba ad, oe=a2, oc=1-a, ce=a, oe squared + oc squared = ce squared, a, oe squared + OC squared = CE squared, A, because a is less than 1, a value is omitted.

exists, can be found, and when oe=oc it is parallel, so a 2=1-a, and a is 2 3,.

I, if there is anything I don't know about mathematics in the future, you can ask me.

In general, if the relationship between two variables x and y can be expressed in the form of y k x (k is a constant, k ≠ 0), then y is said to be an inverse proportional function of x. Because y=k x is a fraction, the value range of the independent variable x is x≠0. And y=k x is sometimes written as xy=k or y=kx-.

The inverse proportional function expression y k x where x is the independent variable and y is a function of x.

y=k/x=k·1/x

xy=ky=k·x^-1

y=k x (k is a constant (k≠0), x is not equal to 0) [this paragraph] the value range of the independent variable of the inverse proportional function k ≠ 0; In general, the value range of the independent variable x is all real numbers of x ≠ 0; The range of values of the function y is also all non-zero real numbersThis paragraph] Inverse Proportional Function Image The image of the inverse proportional function is hyperbola, and the curves are getting closer and closer to the x and y axes but do not intersect (k≠0). This paragraph] inverse proportional function properties 1When k>0, the images are located separately.

1. Three quadrants; When k>0, the images are located separately.

2. Four quadrants.

2.When k > 0. Within the same quadrant, y decreases as x increases; When k < 0, y increases with x in the same quadrant.

When k>0, the function is a subtraction function on x<0 and a subtraction function on x>0. When k<0, the function is an increasing function on x<0 and an increasing function on x>0.

Define the domain as x≠0; The value range is y≠0.

3.Because in y=k x(k≠0), x cannot be 0 and y cannot be 0, so the image of the inverse proportional function cannot intersect with the x-axis or with the y-axis.

4.On an inverse proportional function image, take two points p, q, and pass points p and q as parallel lines of the x-axis and y-axis respectively, and the area of the rectangle enclosed by the coordinate axis is s1, and s2 is s1 s2=|k|

5.The image of the inverse proportional function is both axisymmetric and centrally symmetrical, and it has two axes of symmetry y=x y=-x (i.e., the bisector of the first, third, second and fourth quadrants), and the center of symmetry is the coordinate origin.

6.If the proportional function y=mx and the inverse proportional function y=n x intersect at the points a and b (m and n have the same sign), then the two points a b are symmetrical with respect to the origin.

7.Let there be an inverse proportional function y=k x and a primary function y=mx+n in the plane, so that they have a common intersection, then b +4k·m (not less than) 0.

8.The asymptote of the inverse proportional function y=k x: x-axis and y-axis.

9.The inverse proportional function is symmetric with respect to the positive proportional function y=x, y=-x axis, and symmetric with respect to the origin center.

10.In reverse proportionality, a point m makes perpendicular lines to x and y respectively, and intersects q and w, then the area of the rectangular mwqo (o is the origin) is |k|

(1) y1 is proportional to x, then y1=ax can be set

y2 is inversely proportional to x, then y2=b x

y=y1+y2=ax+b/x

When x=1, y=4;When x=2, y=5

Substituting gets: 4=a+b

5=2a+b/2

Solution: a=2, b=2

So: y=2x+2 x

2) When x=-2, y=-4-2, 2=-5

If AK is the smallest, the intersection point of the hyperbola and AB is point B, and K=1

When k is maximum, the intersection point of the hyperbola and ab is point a, and k=3

So choose A

Since the ordinate of one of the intersections is 6, 3x-2k=(k-3) x=6, and the above equation is equivalent to a system of equations, which is solved to x=-4 3 (the abscissa of one of the intersections), k=-5.

y1=3x+10,y2=-8/x.

I won't draw on this, I can only answer:

3x+10<-8 x, the square of x on both sides, and the inequality does not change.

3x to the power + 10x to the square + 8x<0

x(x+2）(3x+4)<0

x<-2 or -4 3

All I can say is that I didn't even graduate in math.

This seems to be a question about coordinate values, bring in the 6, 6x1=3x-2k : 6x2=(k-3) x

3x 》6 x》2

When x is equal to 2, k = 0.

Left and right: 1:2

I'm sorry, I'm really bad at math, it's normal to be wrong, please weigh it yourself. The figure is gone、,

Such questions can only be used on the test paper, and are not useful at all in practice, and may be useful, but rarely

I really don't understand why those teachers have to call us useless things, a lot.

Education in China is to teach us useless knowledge, but to ignore useful things, such as our morality, politics, etc

o(∩_o~

By question: 3x-2k=(k-3) x

The ordinate is 6, substituting 6 into y1 to get 6=3x-2k to get x=(6+2k) 3 Substituting the obtained x into the top equation can find k

The analytic formula of the two functions is solved.

If you need a diagram, I can draw it and send it to you.

Other than that. You're wrong about the one upstairs ...

y=k1 z, z=k2 x, substituting z=k2 x into y=k1 z gives y=k1 k2 multiplied by x, so y is a proportional function of x.

Solution: From the known obtained, y=m z, z=n x, (m,n is constant), then there is y=(m n)*x (m n is constant), so y is a proportional function of x.

Because y = k of z, and k of z = x of k, then y = k of x

In order to facilitate the sale of tickets for passengers, and at the same time save costs, the number of ticket windows is often determined according to the passenger flow, assuming that each window can sell an average of 60 tickets per hour, and when 8 windows are opened, it takes 5 hours to make all the passengers who buy tickets on the day buy tickets.

1) How many tickets were sold on the day?

A total of 2,400 tickets were sold on the day.

2) When setting up x ticket windows, it takes y hours for all passengers who purchased tickets on the same day to buy tickets, and try to find the functional relationship between y and x.

60＊x*y=2400

The functional relationship between xy=40y and x is xy=40

3) If all the passengers who are going to buy tickets on the same day within 3 hours have bought their tickets, then at least how many ticket windows should be developed?

At least 14 ticket windows will be developed.

Solution: 1, a total of 60 8 5 = 2400 tickets were sold on the same day.

2. According to the title y=2400 60x=40x.

3, because when y=3 x=40 3. Therefore, when 14 windows are developed, passengers are guaranteed to buy tickets within 3 hours.

(1) The total number of tickets sold on the day: 60. Hours * 8 sheets * 5 hours = 2,400 sheets.

2）60 * x * y = 2400 y = 40/x

3) The number of open windows is (set the number of open windows to x): 60 * x * 3 = 2400 x = 2400 60 * 3 = 14

（1）60×8×5=2400

2) 60xy=2400, i.e., xy=40, or, y=40x, or, x=40y

3) With x=40 y, y=3, then, x=40 3=, i.e. at least 14 windows.

The first question, 60*8*5=2400 sheets.

Question 2, y=40 x

Question 3, let y=3, so x=40 3=, take 14 hope it can help you.

1) 60 8 5 2400 (sheets) (2) xy 60 2400 y = 2400 (60 x) y = 40 x (3) when y = 3 x = 40 3 so develop at least 14 windows.