Ad
related to: real life examples of functions and non functions
Search results
Results From The WOW.Com Content Network
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
In mathematics, a real-valued function is a function whose values are real numbers. In other words, it is a function that assigns a real number to each member of its domain . Real-valued functions of a real variable (commonly called real functions ) and real-valued functions of several real variables are the main object of study of calculus and ...
The image of a function f(x 1, x 2, …, x n) is the set of all values of f when the n-tuple (x 1, x 2, …, x n) runs in the whole domain of f.For a continuous (see below for a definition) real-valued function which has a connected domain, the image is either an interval or a single value.
A real-valued function of a real variable is a function that takes as input a real number, commonly represented by the variable x, for producing another real number, the value of the function, commonly denoted f(x). For simplicity, in this article a real-valued function of a real variable will be simply called a function. To avoid any ambiguity ...
[note 2] For example, a "function from the reals to the reals" may refer to a real-valued function of a real variable whose domain is a proper subset of the real numbers, typically a subset that contains a non-empty open interval.
Special functions: non-elementary functions that have established names and notations due to their importance. Trigonometric functions: relate the angles of a triangle to the lengths of its sides. Nowhere differentiable function called also Weierstrass function: continuous everywhere but not differentiable even at a single point.
In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x 1/n).
Well-known examples of convex functions of a single variable include a linear function = (where is a real number), a quadratic function (as a nonnegative real number) and an exponential function (as a nonnegative real number). Convex functions play an important role in many areas of mathematics.