A school needs to hold a student congress, which stipulates that each class selects one representative for every 10 students. When the remainder of the number of students divided by 10 is greater than 6, another representative will be selected. Then, the functional relationship between the number of Representatives y elected by each class and the number x of students in the class can be expressed as () A. y=[x10]B. y=[x+310]C. y=[x+410]D. y=[x+510]

A school needs to hold a student congress, which stipulates that each class selects one representative for every 10 students. When the remainder of the number of students divided by 10 is greater than 6, another representative will be selected. Then, the functional relationship between the number of Representatives y elected by each class and the number x of students in the class can be expressed as () A. y=[x10]B. y=[x+310]C. y=[x+410]D. y=[x+510]

According to the rule, 10 selects a representative. When the remainder of each class divided by 10 is greater than 6, another representative can be added, that is, when the remainder is 7, 8 and 9, one representative can be added, that is, X has to enter one place, so the minimum should be 3. Therefore, the integer function can be expressed as y = [x + 310], or special value method can be used. If x = 56, y = 5, exclude C and D, if x = 57, y = 6, exclude a; therefore, select B

The model and application of function in senior one mathematics (compulsory one)
When a family (father, mother and children) travel to a certain place, travel agency a said: if the father buys a full ticket, the rest of the family members can enjoy a half ticket discount. Travel agency B said: family travel is group ticket, calculated by 2 / 3 of the original price. The original prices of the two travel agencies are the same. After the implementation of the preferential policies of the two travel agencies, the fee expressions with the number of children as the variable are listed, And compare which one is more favorable

If the original price of the two travel agencies is X Yuan and the child is a person, then:
Y a = x + 1 / 2x * (1 + a) = 3 / 2x + 1 / 2aX
Y B = 2 / 3x * (2 + a) = 4 / 3x + 2 / 3ax
When y a = y B, a = 1, you can choose any one
When y a > y B, a > 1 is more cost-effective
When y a

It is predicted that the price of an agricultural product will continue to rise in the early and later stages of the market due to short supply, and in the medium term, the price will continue to fall due to oversupply. Suppose the market time is x (x 4, x = 0 means October 1, and so on), there are three kinds of price simulation functions: ① f (x) = B · a ^ X; ② f (x) = BX ^ 2 + ax + 1; ③ f (x) = x (x-a) ^ 2 + B (where a and B are constants, a〉1).
(1) in order to accurately study its price trend, which price simulation function should be selected? Why?
(2) if f (0) = 1, f (2) = 3, the analytic expression of the selected function is obtained

(1) (2) from the meaning of the question: F (0) = b = 1F (2) = 2 * (2-A) ^ 2 + B = 3 bring B = 1 into f (2), then 2 * (2-A) ^ 2 + 1 = 3 (2-A) ^ 2 = (3-1) / 2 = 1A = 1 or a = 3 because a > 1, so a

It's about the representation of functions
1. It is known that f (x) is a quadratic function and satisfies f (0) = 1, f (x + 1) - f (x) = 2x
2. It is known that a and B are constants, if f (x) = x & sup2; + 4x + 3, f (AX + b) = x & sup2; + 10 + 24, then 5a-b=

1.f(x)=ax^2+bx+cf(0)=1:1=0+0+c,∴c=1∴f(x)=ax^2+bx+1f(x+1)-f(x)=2x：a(x+1)^2+b(x+1)+1-ax^2-bx-1=2x2ax+a+b=2x2a=2,a+b=0a=1,b=-1∴f(x)=x^2-x+12.f(x)=x^2+4x+3f(ax+b)=x^2+10x+24(ax+b)^2+4(ax+b)+3=x^2+10x+...

Given that f (x) is a quadratic function and satisfies f (0) = 1, f (x + 1) - f (x) = 2x, the expression of F (x) is obtained

Let f (x) = AX2 + BX + C, and let f (0) = 1 (f (0) = 1.let f (x) = AX2 + BX + 2 + BX + B (x + 1) = a (x + 2 + 2) 2 + B (x + 1) + 1 = a (x + 2) 2 + B (x + 1) Let f (x) = 1 (f (x) = 1 (x) = AX2 + BX (2 + BX (x) = AX2 + BX (2 + BX) 2 + BX + BX + 2 + BX + BX + BX + 1 + 1 + 1 + 1-1-ax2 + B2 + B2 + B2 + BX (x (x (1) - f (x (x + 1) - f (x (1) - f (1) - f (x (x (x (1) - f (x (x (1) - f (x (x) (2x2x2x x x x x \x + 1

The diameter of the bottom of a cylindrical container is DCM and the height is HCM. Now some solution is injected into the container at the speed of vcm3 / s. The analytic expression of the function of the solution height xcm with respect to the injection time Ts is obtained, and the definition and range of the function are written out

According to the meaning of the topic, there is π (D2) 2x = VT, that is, x = 4V π D2T, obviously 0 ≤ x ≤ h, that is, 0 ≤ 4V π D2T ≤ h, then 0 ≤ t ≤ h π d24v is obtained, and the definition domain of the function is [0, H π d24v] and the value domain is [0, H]

On the representation of function
It is known that f (x) = {1, X ≥ 0 - 1, X

When x ≥ - 2, x + 2 ≥ 0, then f (x + 2) = 1
If x + (x + 2) * f (x + 2) = x + (x + 2) = 2x + 2 ≤ 5, then - 2 ≤ x ≤ 3 / 2
When x ＜ - 2, x + 2 ＜ 0, then f (x + 2) = - 1
If x + (x + 2) * f (x + 2) = x - (x + 2) = - 2 ≤ 5, then x ＜ - 2
In conclusion, X ≤ 3 / 2

Solving three problems about function and its representation in senior one mathematics
1. Given f (√ x-1) = x + 1, find the expression of F (x)
2. Given the function f (x) = x2-4x + 3, find f (x + 1)
3. Given that the quadratic function f (x) satisfies f (0) = 2, f (x + 1) - f (x) = X-1, find the interpretation of F (x)
The √ in the first question means root

Let √ X-1 = t √ x = 1 + T, x = (1 + T) 2F (T) = (1 + T) 2 + 1, that is, f (x) = (1 + x) 2 + 12. If f (x) = x2-4x + 3, find f (x + 1). F (x) = (x-1) (x-3) f (x + 1) = (x + 1-1) (x + 1-3) = x (X-2) 3. If f (x) satisfies f (0) = 2, f (x + 1) - f (...)

What is the number of zeros of a function,

The number of intersections of function and X axis
The number of solutions equivalent to f (x) = 0

How to judge the number of zeros of a function

First find the initial value of the function, and then find the first derivative to see whether it is monotonic increasing or decreasing. If it is not monotonic, then find the second derivative to find its inflection point, and then draw the general graph of the function according to the above three points