① Matching method: transform it into a quadratic function and evaluate it by using the characteristics of the quadratic function; Often converted into:; (2) Inverse solution: the value range obtained by inverse solution is expressed by and then obtained by solving inequality; Commonly used in solving, such as: (4) substitution method: transforming variables into functions of assignable fields and returning to ideas; ⑤ Triangular Bounded Method: Transform it into a function containing only sine and cosine, and use the boundedness of trigonometric function to find the domain; ⑥ Basic inequality methods: transformation and modeling, such as: using the average inequality formula to find the domain; ⑦ Monotonicity method: The function is monotonous, and the domain can be evaluated according to the monotonicity of the function. ⑧ Number-shape combination: According to the geometric figure of the function, the domain is found by the method of number-shape combination.

The definition domain and value domain of the linear function y=ax+b(a 0) are r; The definition domain of the inverse proportional function is {x|x≠0} and the value domain is {y | y≠0 }；; When a >, the domain of quadratic function is r; 0, the range is {y|y≥(4ac-b? 0? 5)/4a }； When a<0, the range is {y|y≤(4ac-b? 0? 5)/4a} cases 1. Find the range1y = 3x+2 (-1≤ x ≤1) solution of the following function: ①∫- 1≤x≤ 1, ∴-3.0 So f (x 0? 5-6x+ 12 is increasing function in x∈, so the range of f (x) min = f (4) = 4f (x) max = f (6) =12f (x) is because the symmetry axis x =-b/2a =-(-). 0 so f(x)=x? 0? 5-6x+ 12 is a decreasing function in x∈ and a increasing function in x ∈ (3 3,5), so f(x)min=f(3)=3, f(0)= 12 f(5)=7. -3)y = 8(-3≤x & lt； 5) y=2x-2(x≥5) Self-painted image As can be seen from the figure, the value range of Y = | x+3 |+| x-5 | is [8, +∞) 6. Using boundedness to find the range solution of Y = 3 x/( 1+3 x). 0 so y/( 1-y)>0 is 0.