Monotonicity of a function means that as X becomes larger, Y becomes larger, indicating that the function is increasing and Y becomes smaller, indicating that the function is monotonous. Symbolic representation: refers to arbitrarily taking x 1, x2, X 1 < X2 in the definition domain. Comparing the sizes of f(x 1) and f(x2), it is a monotonic function for the image to keep rising or falling from left to right, and it is a increasing function for the image to keep rising.
Method of judging the increase or decrease of function
1, basic function method
The method of judging the monotonicity of a function by using the monotonicity of the familiar basis functions (linear, quadratic, inverse proportional, exponential, logarithmic, trigonometric and other functions) is called the basis function method.
2. Mirror image method
The method of judging monotonicity of function by using function image is called image method. The image gradually rises from left to right.
3. Definition method
The method of judging the monotonicity of a function by the definition of monotonicity is called definition method. Let x 1, x2 ∈ d, x 1
This process is to take values-produce differences-deform-judge symbols-and draw conclusions. In fact, this is also the proof process of monotonicity.