High school mathematics knowledge points: common function value domain

The value range of y=kx+b(k≠0) is r.

The value range of y=k/x is (-∞, 0)∩(0,+∞).

The value range of y=√x is x≥0.

y=ax？ +bx+c when a>0, the range is [4ac-b? /4a，+∞)；

When a<0, the range is (-∞, 4ac-b? /4a]

Mathematics knowledge points in senior high school: the judgment method of function value domain

(1) collocation method: Use the collocation method of quadratic function to find the domain, and pay attention to the range of independent variables.

(2) method of substitution: Algebra or trigonometric method of substitution is often used to replace a given function with another function whose value range is easy to determine, so as to get the original function range, such as y = ax+b+_ √ CX-d (A, B, C, D are constants, and ac is not equal to 0).

(3) Discrimination: If the function is a fractional structure, the denominator contains the unknown number x? , often use this method. Usually, the denominator is removed and transformed into a quadratic equation, and then the range of y is determined by the discriminant △≥0, which is the range of the original function.

(4) Inequality method: When using a+b≥2√ab (where A, b∈R+) to find the function range, we should always pay attention to the conditions under which the inequality is established, that is, "one positive, two definite, three-phase and so on".

(5) Inverse function method: If the range of the original function is not easy to be directly solved, we can consider the definition range of its inverse function, and determine the range of the original function according to the characteristics of the exchange between the definition range and the range of two functions that are inverse functions, such as the range of y=cx+d/ax+b(a≠0) function, which can be either the inverse function method or the separation constant method.

(6) Monotonicity method: first determine the domain of the function, and then find the domain of the function according to its monotonicity, which is often used for the function y = x+p/x (p > 0) Monotonicity: the left open and right closed interval with increasing interval (-∞, -√p) and the left closed and right open interval with decreasing interval (√p,+∞).

(7) Number-shape combination method: analyze the collective meaning expressed by the resolution function, and determine the range according to its image characteristics.