Functions are usually represented by symbols, such as f(x), where f represents the function name, x represents the input value and f(x) represents the output value. Functions can be used to describe various mathematical problems, including geometry, algebra, calculus and so on.
The definition of function includes domain, range, image and analytical formula. The definition domain refers to the set of input values of the function, and the value domain refers to the set of output values of the function. An image refers to a graph of a function in a coordinate system, which is a collection of points composed of input values and output values of the function. Analytical formula refers to a mathematical formula that describes a function in the form of a formula or a table.
Function was originally translated by Li, a mathematician of Qing Dynasty in China, in his book Algebra. He translated this way because "whoever believes in this variable is the function of that variable", that is, the function means that one quantity changes with another quantity, or that one quantity contains another quantity.
Characteristics of functions
1, boundedness: let the function f(x) be defined on the interval x, if there is m >；; 0, for all X belonging to the interval X, there is always |f(x)|≤M, then f(x) is bounded on the interval X, otherwise F (x) is unbounded on the interval.
2. Monotonicity: Let the domain of the function f(x) be D, and the interval I is included in D ... If for any two points in the interval x 1 and x2, when X 1
If for any two points x 1 and x2 on the interval I, when X 1
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