What are the knowledge points of high school functions, and what are the knowledge points of high sc

The knowledge points of high school math functions are as follows:

1. If the function is an analytic formula determined by the actual meaning, the range of its values should be determined according to the actual meaning of the self-congratulatory variable.

2. If f(x) and g(x) are both increase (decrease) functions in a certain interval, then f(x)+g(x) are also increase (decrease) functions in this interval.

3. If the domain of the function f(x) is symmetrical with respect to the origin, then f(x) can be expressed as f(x)=1 2[f(x)+f(-x)]+1 2[f(x)+f(-x)], which is characterized by the sum of an odd function and an even function at the right end.

4. If an odd function is defined at x=0, then f(0)=0, and if a function y=f(x) is both an odd function and an even function, then f(x)=0 (vice versa).

5. When the pumping speed f of the pool is constant, the amount of water g in the pool is a function of the pumping time t. Set up the original water model in the pool.

1. Definition of the zero point of the function

1) For the function y=f(x), we call the real root of the equation f(x)=0 the zero opener point of the function y=f(x).

2) The equation f(x)=0 has a real root = function y=f(x) and the image has an intersection point with the x-axis = the function y=f(x) has a zero point. Therefore, to determine whether a function has zero points and how many zero points there are is to determine whether the equation f(x)=0 has real roots and how many real roots there are. Finding the zero point of the function:

Solve the equation f(x)=0, and the resulting root of the real number is the zero point of which f(x) is earlier.

3) Variable zero and unchanged zero.

If the function f(x) is on the left and right sides of the zero point x0, the zero point is said to be the variable zero point of the function f(x).

If the function f(x) has the same sign on the left and right sides of the zero point x0, the zero point is said to be the invariant zero point of the function f(x).

If the function f(x) is over the interval =a,b=. If the image is a continuous curve, then f(a)f(b)=0 is a sufficient and unnecessary condition for f(x) to have a zero point in the interval =a,b=.

2. Determination of the zero point of the function

1) Zero-point existence theorem: If the image of the function y=f(x) in the interval [a,b] is a continuous curve, and there is f(a)=f(b)=0, then the function y=f(x) has zero points in the interval =a,b=, that is, there is x0=(a,b), such that f(x0)=0, and this x0 is the root of the equation f(x)=0.

2) The method of determining the number of zeros of the function y=f(x) (or the number of real roots of the equation f(x)=0).

Algebraic: the zero point of the function y=f(x)=the root of f(x)=0;

For equations that cannot be found using the root formula, it can be related to the image of the function y=f(x) and the zero point can be found by using the properties of the function.