Elementary 3 Mathematics, Problems with Inverse Proportional Functions

where y=m+1 x is y=(m+1) x?If yes, then:

Solution: The intersection of the function image y=x+m and y=(m+1) x,(m≠1) in the first quadrant is p(a,3), then x=a>0, then:

3=a+m，3=(m+1)/a；Simultaneous solution: m=2, a=1;

Then the analytic formulas for the primary function and the inverse proportional function are respectively:

y=x+2 and y=3 x

p on two function images, so.

a+m=3m+1)/a=3

Eliminate m3-a = 3a-1

a=1, so a=1, m=2

y=x+2, and y=3 x

It can be obtained according to the intersection.

3=a+m3=m+1/a

Get a = 1m = 2 or 4

Because a>0 is obtained in the first quadrant, a=-1 is rounded.

y=x+2y=1/x+2

y=x+m vs. y=m+1 x

Simultaneous equation yields, x+m=(m+1) x

x^2+mx-(m+1)=0

Solve this equation to give x=1 or -(m+1).

When x=1, substitute y=x+m

There is 1+m=3

So m=2, and when x=-(m+1), it is not true, so a is 1 second question, so they are y=x+

1.Substituting (a,3) into y=x+m and y=m+1 x to get a=1 or -1 (rounding).

The analytic expression of the m=2 primary function is y=x+2

The analytic expression of the inverse proportional function is y=2+1 x

3=a+m3=m+1/a

Subtract 2 formulas to give a-1 a=0

So there is a 2-1=0

a+1)(a-1)=0

So a = 1

It's in the first quadrant again, so a=1

3=1+m, so m=2

So the analytic expression of the primary function is y=x+2

The analytic expression of the inverse proportional function is y=2+1 x

1.Solution: The image of y=k x with y=3 x is symmetrical with respect to the x-axis.

k = 3 point a ordinate 0 a point in the second quadrant.

Bring y=3 into then x=-1 m=-1

Bring (-1,3) in and get a=-1

2.①.Solution: Derived from the question.

kx=5-k x brings x=2 in, and the solution is k=1y=4 x and x=2 is cleverly brought in, y=2

The coordinates of the two intersections are (2,2) and (-2,-2).When x1y2

3.①.Substituting (1,5) into two functions respectively, the solution is k=5 m=2, and the analytic formula of the inverse proportional function is y=5 x x the analytic formula of the primary function is y=3x+2, and the inverse proportional function is axisymmetric graph.

The other intersection coordinates are (-1, -5).

4.Let y=k x, and bring in the coordinate posture of point a.

Then k=12 The analytic formula of the inverse proportional function is y=12 x, and let y=k1x+b(k1≠0).

Bring the coordinates of A and B into the wide search.

The solution gets k=-2 b=10 y=-2x+10 and then it won't.

Hope it helps.

It is known that the analytic formula of the inverse proportional function is y=mxBring a(2,6) into 6= and then b(3,4) into Xunhe, 4= So m takes the rolling state value range is 3 4

You can ask the teacher What the teacher says is clearer than on the Internet

y= -8 x and y= -x+2 to solve the system of equations: a and b are (4,-2),(2,4).

y= -x+2 with the intersection point of the x-axis (2,0) area of the triangle AOB = 1 2*OA*b point ordinate = 4

-8 x=-x+2 The x1=4 x2=-2 solution yields the coordinates a b 4,-2 2,4 respectively by bringing in arbitrary equations

Let the equation y=kx+b bring the ab coordinates into the solution and the focal point of y=-x+2 and the x-axis is 2,0

s triangle aob=2 4 half +2 2 half = 6 refinement!

Solution: (1) Forming a system of equations with y=- 8x and y=-x+2, solution: (1) solving the system of equations y=-8 x y=-x+2 to obtain x1=4 y1=-2 and x2=-2 y2=4 The coordinates of the two points of a and b are a(-2,4) and b(4,-2) (2) The coordinates of the intersection of the line y=-x+2 and the y-axis d are (0,2), S aod= 12 2 2=2, S bod= 12 2 4=4, S aob=2+4=6

1)-x+8=k x solution x 2-8x+k=0 has a solution So >=0 solution 02) let a be (x1,y1) b is (x2,y2)s=x2*8 2-x1*8 2=(x2-x1)*4 from x 2-8x+k=0 x2+x1=8 x1x2=k(x2-x1) 2=(x1+x2) 2-4*x1*x2=64-4kx2-x1=2 16-k

s=8√16-k

y1=k1x, y2=k2 x, when x=1, k1-k2=-14, when x=4, 4k1-k2 4=3, you can find k1 and k2, the relationship between y and x comes out, you calculate it yourself, and the next few questions will be solved.

1.Let t=u k and substitut k=40 so t=u 40

You should ask the teacher, classmates, don't rely on the Internet, the teacher is very helpful to you.

The coordinates d(-6,9), a(0,12), b(-6,15) are obtained, and the linear equation ad:y=x 2+12, ob:y=-5 2 *x

The intersection point e(-4,10), so k=xy=-40

1 According to the proportional function relation, the coordinates of a can be set to be (x, x 2), and the area of the triangle OAB is 1, then there is (x*x 2) 2=1, and the solution is x=plus or minus 2 (rounding -2), so the coordinates of a are (empty and hidden boy 2,1), and substituting it into the inverse proportional formula to get k=2, and the inverse proportional function formula can be obtained.

2. P(x,0) can be set, from the above we can know that with brother a(2,1),b(1,2), according to the formula of the distance between two points, the formula of pa+pb can be listed, and then the value of x when and the minimum bucket is obtained.

1 According to the proportional function relationship, the liquid state trace formula can set a sitting trace bold mark is (x, x 2), and the area of the triangle oab is 1, then there is (x*x troubled and 2) 2=1