Search results
Results from the WOW.Com Content Network
(In old texts, such a domain was called the domain of definition of the function.) Functions can be classified by the nature of formulas that define them: A quadratic function is a function that may be written f ( x ) = a x 2 + b x + c , {\displaystyle f(x)=ax^{2}+bx+c,} where a , b , c are constants .
The term domain is also commonly used in a different sense in mathematical analysis: a domain is a non-empty connected open set in a topological space. In particular, in real and complex analysis , a domain is a non-empty connected open subset of the real coordinate space R n {\displaystyle \mathbb {R} ^{n}} or the complex coordinate space C n ...
In complex analysis, a complex domain (or simply domain) is any connected open subset of the complex plane C. For example, the entire complex plane is a domain, as is the open unit disk, the open upper half-plane, and so forth. Often, a complex domain serves as the domain of definition for a holomorphic function.
The names for the degrees may be applied to the polynomial or to its terms. For example, the term 2x in x 2 + 2x + 1 is a linear term in a quadratic polynomial. The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial. Unlike other constant polynomials, its degree is not zero.
A codomain is part of a function f if f is defined as a triple (X, Y, G) where X is called the domain of f, Y its codomain, and G its graph. [1] The set of all elements of the form f(x), where x ranges over the elements of the domain X, is called the image of f. The image of a function is a subset of its codomain so it might not coincide with it.
For example, the polynomial x 2 y 2 + 3x 3 + 4y has degree 4, the same degree as the term x 2 y 2. However, a polynomial in variables x and y , is a polynomial in x with coefficients which are polynomials in y , and also a polynomial in y with coefficients which are polynomials in x .
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
The subdomains together must cover the whole domain; often it is also required that they are pairwise disjoint, i.e. form a partition of the domain. [5] In order for the overall function to be called "piecewise", the subdomains are usually required to be intervals (some may be degenerated intervals, i.e. single points or unbounded intervals).