Judging inverse proportion function If the area of the trapezoid is fixed, is the median line inversely proportional to the height?

Judging inverse proportion function If the area of the trapezoid is fixed, is the median line inversely proportional to the height?

Inverse proportional function
reason
Trapezoidal area
=(upper bottom + lower bottom) × height △ 2
=Median line × height
So it's an inverse scale function

Judgement of inverse proportion function
What is the inverse proportion function in the following relations?
A. y=k/x B.y=x/2 C.y=-2/3x D.y=3/x-2
Why not a?

When k = 0, it is not an inverse proportional function

The definition of positive proportion function

You need to see it for a long time, not y = ax + B

How to find positive proportion function? Definition?

Let the analytic expression of positive proportion function be y = KX
As long as you know a set of data, you need the value of K
Definition: a function in the form of y = KX (K ≠ 0) is called a positive proportion function

What is the meaning of positive scale function

① Definition of positive scale function:
A function of analytic form y = KX (K ≠ 0) is called positive proportional function, where k is called slope
(2) image and properties of positive scale function
(1) the image is a straight line passing through (0,0), (a, AK) points
(2) when K0, the image is in the first and third quadrant, and Y increases with the increase of X

The definition and formula of positive proportion function

Generally, the relation between two variables X and y can be expressed as a function of y = KX (k is a constant and K ≠ 0), then y is called the positive proportional function of X
Positive proportion function is a special form of linear function, that is, in the linear function y = KX + B, if B = 0, that is, the so-called "intercept on Y axis" is zero, then it is a positive proportion function. The relationship of positive proportion function is expressed as: y = kx (k represents slope)

On the concept of positive proportion function!
The function y = KX (k is a constant not equal to 0) whose domain is () is called positive proportional function, where the constant k is called proportional coefficient!

In general, the relationship between two variables X and y can be expressed as a function of y = KX (k is a constant, and K ≠ 0), then y is called the positive proportion function of X. The positive proportion function belongs to the first-order function, but the first-order function is not necessarily a positive proportion function. The positive proportion function is a special form of the first-order function, that is, if B = 0 in the first-order function y = KX + B, the so-called "intercept on the Y axis" is zero, When k > 0 (one or three quadrants), the larger K is, the closer the distance between the image and the y-axis is. The value of function y increases with the increase of independent variable x. when k < 0 (two or four quadrants), the smaller K is, the closer the distance between the image and the y-axis is. When the value of independent variable x increases, the value of function y decreases gradually
Domain of definition
R (real number set)
range
R (real number set)
Parity
Odd function
Monotonicity
When k > 0, the image is located in the first and third quadrants, and Y increases with the increase of X (monotonic increase), which is an increasing function;
When k

Abstract function. Why is f (x + y) = f (x) + (y) equivalent to y = KX (positive proportion function)? And if it is deformed
F (XY) = f (x) f (y) ---- the nth power of y = x (exponential function)
F (XY) = f (x) + F (y) ---- y = logarithm of X with base a (logarithm function)
F (x + y) = f (x) f (y) ---- power function of y = a

Function can be written like this, f (x) = y = KX, then f (x + y) = K (x + y), f (x) = KX, f (y) = KY can be added!
The following are the properties of functions

Which two points does the positive scale function pass through?
If a function passes through (0, b) and (- B / K, 0), then that function passes through (0,0) and (?,)

The image of linear function y = KX + B (k, B are not zero) must pass through a point (- B / K, 0) but not the origin. The image of positive scale function y = KX (k is not zero) must pass through the origin (0,0)

The deformation of abstract function
See that there are f (x2) - f (x1) = f (x2-x1) and f (- 3) = - f (3) = - 3f (1) in the book. Are these deformations right? Do we need to combine the formula given by the title to realize these deformations? Besides, are there other similar deformations?

For example, f (x 2) - f (x 1) = f (x 2-x 1) does not have a general rule, which is related to the condition of the title. For example, the title gives f (X-Y) = f (x) - f (y)
And f (- 3) = - f (3) = - 3f (1), look at this formula is not too much significance. Such as odd function f (x) = - f (- x), even function f (x) = f (- x), inverse function deformation is you really want to master, with universal significance. Learning them combined with the period will easily confuse people
Other common forms of abstract functions are
Power function: F (XY) = f (x) f (y)
Positive scale function: F (x + y) = f (x) + F (y)
Logarithmic function: F (x) + F (y) = f (XY)
Trigonometric function: F (x + y) + F (X-Y) = 2F (x) f (y)
Exponential function: F (x + y) = f (x) f (y)
Periodic function with period n: F (x) = f (x + n)