1: direct method: starting from the range of independent variables, the range of values can be deduced, that is, it can be seen directly. Doesn't this need an example?

2. Take the separation constant method as an example: y = (1-x 2)/( 1+x 2) solution, y = (1-x2)/(65438).

3. The matching method (or the maximum value method) finds the maximum value and the minimum value, so the range comes out. Example: y = x2+2x+3x∑- 1, first formulate 2, and get y = (x+ 1) 2+ 1.

4. Discriminant method, using the idea of equation, has a real root evaluation domain according to quadratic equation. Sorry, I forgot to copy the examples when I took notes, but this method is not very common.

.. 5. method of substitution: Examples of functions with roots: y = x-√ (1-2x) let √ (1-2x) = t (t ≥ 0) ∴ x = (1-t2)/2 ∴.

6. Mirror method, drawing directly to see the range Example: y = | x+ 1 |+√ (x-2) 2 This is a piecewise function, and the range can be seen at a glance after drawing.