There are three function expressions

There are three function expressions

There are three ways to express a function: analytic formula (using mathematical formula to express the functional relationship between two variables), image method (using image in coordinate system to express the functional relationship between two variables), list method (using table to express the functional relationship between two variables). Expression is mathematical formula, that is, the mathematical formula expressed by analytic formula

Symmetric function expression
Given that a function is symmetric to x = a, what expression can we get about this function?

Let y = f (x)
Then the image of y = f (x) is symmetric with respect to the line x = a
y =f(2a -x).
It is known that,
f(x) =f(2a -x).
= = = = = = = = =
Baidu Encyclopedia:
Image transformation
See: 2. Symmetry transformation (5)

Find the function expression
A store sells a commodity. According to the sales experience, when the price of the commodity is 200 / piece, 60 pieces will be sold every month. When the price of the commodity increases by 10 yuan, one piece will be reduced. And for the sold commodity, 20 yuan freight will be paid for each piece sold. Suppose the price of the commodity is x yuan per month
1. The function relation of commodity y {pieces} sold every month with respect to X (yuan)
2. The sales volume of the goods sold in the store every month is a function of Z (yuan.) with respect to X (yuan)
3. The function relation of the profit w (yuan) of this kind of goods sold by the store every month with respect to X (yuan) is. When the price of each piece of the goods is, w has the maximum value. What is the maximum value

（1）y=60-(x-200)/10
（2）z=[60-(x-200)/10]x
（3）w=[60-(x-200)/10](x-20)=-1/10x^2+82x-1600=-1/10(x-410)^2+15210
When the price of each product is 410 yuan, w has a maximum value of 15210 yuan

Mathematics of the second grade of junior high school
1. Given that y + 2 and X are in positive proportion, and when x = - 1, y = 2, then the functional relationship between Y and X is______ (to calculate the process)

Let the expression be y + 2 = KX
When x = - 1, y = 2
2+2=-1k
So k = - 4
So y + 2 = - 4x
So y = - 4x-2

Mathematics of the second grade of junior high school
A shop bought a batch of shirts. After a trial sale, it was found that if they were sold at the price of 20 yuan per piece, 360 pieces could be sold every month; if they were sold at the price of 25 yuan per piece, 210 pieces could be sold every month. Assuming that the monthly sales volume y (pieces) is a function of the price x (yuan), the expression of the function is_________ .

Let: the expression of a function be
y=kx+b
Substitute the condition into the result
360=20k+b (1)
210=25k+b (2)
(1) - (2) get
150=－5k
K = - 30 is substituted into (1)
b=960
Then the function expression is y = - 30x + 960

On the formula and result of function
Given the image of a function of degree (- 1, - 5), (2,3), find the analytic expression of the function

Let y = KX + B be a linear function
∵ the image is over (- 1, - 5), (2,3)
∴-5=-k+b
3=2k+b
The solution is: k = 8 / 3, B = - 7 / 3
Analytical formula: y = (8 / 3) X-7 / 3

Let y = KX + B be 2

① By substituting x = 2, y = 1; X = 5, y = 7 into the analytic expression of the function, we get
2K + B = 1.5k + B = 7, k = 2, B = - 3
② Then we substitute x = 2, y = 7; X = 5, y = 1 into the analytic expression of the function
2K + B = 7.5K + B = 1, k = - 2, B = 11
The first is k > 0
The second is K

According to the following conditions, the analytic expressions of the function y = KX + B are determined respectively: 1. Y is proportional to x, when x = 5, y = 6; 2. The straight line y = KX + B passes through points (3,6) and points (1,2, - 1,2)

1. Because the positive ratio has to be y = ax,
So B = 0,
Substituting x = 5, y = 6
6=k×5
k=6/5
So the analytical formula is y = 6 / 5x
2. Substituting coordinates
6=3k+b
-1/2=1/2k+b
5 K = 6
k=13/5
So B = - 1 / 2-13 / 10 = - 18 / 10 = - 9 / 5
So the analytical formula is y = 13 / 5x-9 / 5

The analytic expression of the function y = KX is obtained according to the following conditions
(1) When x = 5, y = 6;
(2) The line y = KX + B passes through (3,6) and point (half, negative half)
Please give me a detailed analysis

Let y = KX,
Because x = 5, y = 6,
So k = 6 / 5, that is y = (6 / 5) X

According to the following conditions, the analytic expression of the function y = KX + B is determined. The straight line y = KX + B passes through points (3,6) and points (half, negative half)

6 = 3*k+b
-1/2 = 1/2 * k + b
Simultaneous solution of equations
k = 13/5
b = -9/5
therefore
y = 13/5*x-9/5