Chinese interpretation

The monotonicity of a function is also called the increase or decrease of a function. Monotonicity of a function is a local concept of an interval.

English interpretation

Monotonicity A function y=f(x) is monotonic in the interval (a, b) if it increases or decreases there. Assume that x 1 and x2 are in the interval, and x1<; x2。 If f (x1) <; f(x2)； If f(x 1)> 0, then f(x) decreases; f(x2)。

[Edit this paragraph] increasing function sum subtraction function

Generally speaking, let the domain of the function f(x) be I: if the values of any two independent variables belonging to an interval in I are x 1 and x2, then when X 1 < X2, there will be F (X 1) < F (X2). Then let's assume that f(x) is increasing function in this interval. On the other hand, when X 1 < X2, if the values of any two independent variables belonging to an interval in I are F (x 1) > F (x2), then F (x) is a decreasing function in this interval.

[Edit this paragraph] Monotonicity and Monotonicity Interval

If the function y=f(x) is a increasing function or subtraction function in a certain interval, it is said that the function has (strict) monotonicity in this interval, and this interval is called the monotone interval of the function. At this time, it is also said that the function is monotonic in this interval. In the monotone interval, the image of increasing function is rising, and the image of subtraction function is falling. Note: Monotonicity has the following properties. Legend: ↑ (increasing function) ↓ (subtraction function) ↑+↑ = ↑ The sum of the two increasing function is still increasing function ↑-↓ = ↑ increasing function minus the subtraction function is increasing function ↓+↓ = ↓ The sum of the two subtraction functions is still the subtraction function minus increasing function minus the subtraction function.