A problem about the definition of inverse proportion function If the variable y is positively proportional to X and the variable x is inversely proportional to Z, what is the functional relationship between Y and Z? Online waiting, 4:30 before the answer, urgent! Hurry! Hurry!

The variable y is positively proportional to x, and the variable x is inversely proportional to Z,
So it can be set
y=k1x
x=k2/z
Namely
y=k1 ×k2/z=k1k2/z
therefore
Y is inversely proportional to Z

What does the inverse proportion function mean!
Be specific

Generally, if the relationship between two variables X and y can be expressed as y = K / X (k is a constant, K ≠ 0), then y is the inverse proportional function of X. because y = K / X is a fraction, the value range of independent variable x is x ≠ 0. Sometimes y = K / X is written as xy = k or y = k · x ^ (- 1)

Are inverse proportion function and positive proportion function power functions?
For example, is the negative cubic of y = x an inverse proportional function? Is it the same as the cubic domain of y = x? Is its domain greater than or equal to 0 or only greater than 0?

Inverse proportion function belongs to power function, single power function is not necessarily inverse proportion function, positive proportion function is the same as above, in addition, the definition field of inverse proportion x is not equal to 0

Does a linear function include a positive scale function and an inverse scale function

The form of y = KX + B (K ≠ 0) is called a linear function,
When B = 0, y = KX is called positive proportional function,
The form of y = K / X (K ≠ 0) is called inverse proportional function,
Obviously, the linear function includes the positive scale function, but does not include the inverse scale function

A problem of inverse proportion function and positive proportion function
It is known that y is inversely proportional to χ and Z is positively proportional to y. when χ = 8, y = 1 / 2; when y = 1 / 3, z = - 2. Is Z a function of χ? When χ = 16, what is the value of Z? It should be written vertically

Let xy = K1, z = k2y
Substitute x = 8, y = 2 / 1 into xy = K1 to get
K1=4∴xy=4.y=4/x
Substituting y = 3 / 1, z = - 2 into Z = k2y
K2=﹣6∴z=﹣6y.y=﹣6/z.
6 / z = 4 / x, z = - X / 24. Substitute χ = 16 to get z = - 2 / 3
х Z is a function of χ

What is the relationship between positive scale function and inverse scale function
In the same plane rectangular coordinate system, if an image of an inverse scale function intersects an image of a positive scale function, what is the relationship between the coordinates of those two intersections? Are the abscissa and ordinate opposite to each other? If so, please help to prove. If not, please explain

Let the inverse scale function be y = K / X and the positive scale function be y = k'x
Because there is an intersection point, so K / x = k'x, the solution is x = ± √ (K / K ')
y=±√(KK')
So the abscissa and ordinate are opposite to each other

1 positive proportion function 2 inverse proportion function 3 quadratic function 4 constant function number 5 piecewise function 6 primary function 7 quadratic function, odd function and even function

The odd and even functions are judged according to whether the image is symmetrical about the origin or y-axis
1. 2 is an odd function
3. 7 is an even function
4. 6 is neither an odd function nor an even function
How are three and seven the same?
Generally, you can see by looking at the image

Finding the analytic expression of a quadratic function``
If a quadratic function passes through points (0, - 1), (3,2), the vertex is on the straight line y = 3x-3, and the opening is downward, the analytic formula is obtained``

Let the analytic formula be y = ax ^ 2 + BX + C, because it passes through the point (0, - 1), so C = - 1 and passes through the point (3,2) 2 = 9A + 3b-1 to get a = (1-B) / 3. The vertex of the parabola is [- B / 2a, (- 4a-b ^ 2) / 4A] and the vertex is on y = 3x-3, so (4a + B ^ 2) / 4A = 3B / 2A + 34a + B ^ 2 = 6B + 12ab ^ 2-6b-8a = 0. Substitute a = (1-B) / 3 into 3B ^ 2-10b-8 = 0 (...)

Sum up the relationship between linear function, positive proportion function, inverse proportion function y and X

(1) When k > 0, the function image passes through one or three quadrants and the origin, y increases with the increase of X; when k, 0, the function image passes through two or four quadrants and the origin, y decreases with the increase of X

The relationship between two intersection coordinates of inverse proportion function and linear function
I found that the intersection of inverse proportion function and linear function has the following relationship: suppose the intersection above the X axis is (x, y), then the other is (- y, - x) (note the minus sign). Is this conclusion right or wrong? If it is right, how to prove it? If it is wrong, how to prove it?
Downstairs, what you said is positive proportion and inverse proportion. What I asked is that the law of positive proportion and inverse proportion of ordinary linear function (y = KX + b) is (x, y) (- x, - y)

It should be (- y, - x)~
It's easy to bring a few points in
On the origin symmetry is the relationship between the two intersection points of inverse scale function and positive scale function

A problem about the definition of inverse proportion function If the variable y is positively proportional to X and the variable x is inversely proportional to Z, what is the functional relationship between Y and Z? Online waiting, 4:30 before the answer, urgent! Hurry! Hurry!