Basic Functions are real-valued functions of a real variable. Basic functions can be represented by an analytical expression. At the elementary functions include rational functions, trigonometric functions, exponential and logarithmic functions and their inverse functions.
In general, a function is a mapping between two quantities that accurately assigns to each element of one set is an element of the other.
A function f assigns to each element of a quantitative definition D exactly one element of the target set Z. Assigned for the only the element x ∈ D element of the target set to write in general f (x).
In mathematics, ie a function or sequence that is always greater with increasing function argument or constant (ie never falls), monotonically increasing (or monotonically increasing or isotonic). Accordingly, ie a function or sequence monotonically decreasing (antitone) when it is only smaller or remains constant. The values of the function or the terms of the sequence change anywhere, it is called constant. Strictly increasing (resp. strictly decreasing) are functions or sequences that are only larger (smaller), but are nowhere constant.
A function is called continuous if sufficiently small changes of the argument (argument) to arbitrarily small changes in the function value. This means in particular that no jumps occur in the function values.
A function is called bounded if the function values f(x) does not exceed an upper or lower bound. That if f(x) ≤ M for all real numbers x, then the function f is bounded from above. When M is the smallest integer for which holds, then M is the upper limit of the function f with respect to the analogous definition applies to the lower limit. F(x) for all x is greater than m, then m is the lower limit.