1, direct method.

The so-called direct method is to directly calculate the value range of the function from x, which is suitable for relatively simple function formulas.

2. Matching method.

The matching method is to express the original function with the formula of complete square.

3, the most value method.

There is a prerequisite for the use of the maximum method, that is, it must be a continuous function in a closed interval, so that its maximum and minimum values can be directly obtained.

4. Inverse function method.

Inverse function is to use the reciprocal relationship between the definition domain and the value domain to find the inverse function first and then the value domain of the original function.

5. Separation constant method.

Constants are solved separately by formulas.

6. Alternative methods.

Set the whole formula as an unknown number, find the numerical value in the original formula, and simplify the complex.

7. Discrimination method.

The function is transformed into a quadratic equation about x, and the range of the original function is obtained through the equation with real roots and discriminant. This method is called discrimination.

This kind of problem can be divided into two categories: one is that there is no common factor between numerator and denominator, which can generally be solved by discriminant, but attention should be paid to the two situations in which the quadratic coefficient is zero and not zero; The other is that the numerator and denominator have a common factor. Remove this common factor and go back to the above method to solve. However, it is worth noting that the domain of the function is a problem.

Discriminant method for finding the function value domain-the method of transforming a function into a quadratic equation about x and finding the original function value domain through an equation with real roots and discriminant is called discriminant method.

8. Monotonicity of functions.

Using monotonicity of function to solve. The method of determining the monotonicity of a function in its definition domain (or a subset of the definition domain) and then finding the function value domain. This method is considered by some simple elementary functions composed of exponential function or logarithmic function, and the answer can be obtained directly by using the monotonicity of exponential function or logarithmic function.

There are also some forms, such as whether A and D are the same number, if they are the same number, the monotonous evaluation domain is used, if they are different numbers, the method of replacing the evaluation domain is used; When using important inequality evaluation domains fails, others can use monotone evaluation domains.