Let the function f(x) be defined on the real number set A. If there is a positive number m and the inequality |f(x)|≤M, the function f(x) is bounded on A. If there is no positive number m defined in this way, the function f(x) is unbounded on A.? Let f be a function defined on d. If there is a number M(L), for each x∈D, there is:? (x)≤M(？ (x)≥L)

What's it called? A function with an upper (lower) bound on d, M(L) is called? An upper (lower) bound on d.

Example: sin x function and cos x function are bounded functions on r, because for every x ∈ R there are |sin x|≤ 1 and |cos x|≤ 1.

Extended data:

The bounded function is that f(x) is a function on the interval E. If any x belongs to E and has constants m and m, so that m≤f(x)≤M, it is said that f(x) is a bounded function on the interval E, where m is called the lower bound of f(x) and m is called the upper bound of f(x) on the interval E..

Bounded functions are not necessarily continuous. By definition? There is an upper (lower) bound on d, which indicates the range? (d) is a set of numbers with upper (lower) bounds.

According to the principle of infimum? There is an upper (lower) supremum on the domain. A special case is bounded sequence, where x is the set n of all natural numbers. By who? The function f:R→R defined by (x)=sinx is bounded. As x approaches-1 or 1, the function value becomes larger and larger.

Baidu Encyclopedia Bounded Function