The expression form of high school function

The expression form of high school function

In fact, the function has been talked about in junior high school. Of course, it was the simplest one and quadratic at that time. The most dramatic function in senior high school is actually quadratic function. The general strategy of learning function well is to master the properties of each function, so that it can be used freely and be prepared

How to find the common periodic function

Give me a specific = = general method is based on the period, generally use two periodic conditions, and then solve

Common forms of periodic function and its axis of symmetry
Don't use trigonometric functions, such as f (x) = f (x + 2), f (a + x) = f (A-X)

F (x + a) = f (x), a > 0, period T = a
f(x+a)=-f(x),a>0,T=2a
f(x+a)=1/f(x),a>0,T=2a
f(x+a)=-1/f(x),a>0,T=2a
f(x+a)=f(x+b),T=|a-b|
F (x) satisfies that f (a + x) = f (A-X), and f (x) is symmetric with respect to x = a
F (x) satisfies that f (a + x) = f (b-X), and f (x) is symmetric with respect to (a + b) / 2
Y = f (a + x) and y = f (b-X) are symmetric with respect to x = (a-b) / 2

[function] what are the common inferences about the center of periodic symmetry in functions?
I want to use trigonometric functions to analogize abstract functions, but I still can't see what the central idea is. Let's see OTL for height

First of all, let's make it clear that the axis of symmetry has nothing to do with the center of symmetry. Trigonometric function is only a special case. The midpoint of the two centers of symmetry is the line where the axis of symmetry lies. For function y = f (x), if there is a constant t that is not zero, so that when x takes every value in the domain, f (x + T) = f (x) holds, then

Why the limit of Dirichlet function does not exist?

Jump break point, left and right limits are not equal

How to prove that Riemann function is not differentiable everywhere

Just by definition
The derivatives at rational and irrational points are discussed respectively

The proof of Riemann integrability of bounded function f (x) on [a, b] if and only if f (x) is continuous almost everywhere

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It doesn't mean Baidu knows the views of intellectuals
Answer: huangcizheng
sage
At 16:08 on February 9, it is proved that because f (x) is continuous on [a, b], the maximum value m can be obtained in this interval, and there is a minimum value m, that is, for all x ∈ [a, b], there is m ≤ f (x) ≤ M
So m ≤ f (XI) ≤ m (I = 1,2 ,n）
Because M = nm / N ≤ [f (x1) + F (x2) + +f(xn)]/n≤nM/n=M
According to the intermediate value theorem, there exists ξ ∈ [a, b], such that f (ξ) = [f (x1) + F (x2) + +f(xn)]/n.
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The famous Dirichlet function is defined like this

F (x) = 1, X is a rational number
0 x is an irrational number
It's a piecewise function

Let the quadratic function y = x & # 178; + BX + C satisfy that when x = 1 and x = 5 are equal to the value of Y, find the value of X so that the value of function y is equal to C-8

Because when x = 1.5, y is equal, so the x value of the lowest point is between 1 and 5, which is 3
There are: B / - 2A = 3 and a = 1, so B = -- 6
So: y = x ^ 2-6x + C
There are: x ^ 2-6x = - 8
Er... There's something to go. The first step will be done if you understand it. You can go on with the rest. Ha

Find the minimum value of function f (x) = 2x + 1 / 2x in the interval (0, positive infinity)!

Basic inequality
Because the domain is (0, positive infinity)
So f (x) = 2x + 1 / 2x ≥ 2 √ (2x * 1 / 2x) = 2
The minimum value if and only if 2x = 1 / 2x, i.e. x = 1 / 2