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Topic: Function domain

	Function (mathematics) - Wikipedia, the free encyclopedia
		In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range).
		A very common type of function occurs when the argument (input) and the value (output) are both numbers, the functional relationship is expressed by a formula, and the value (output) of the function is obtained by direct substitution of the argument into the formula.
		The number of computable functions from integers to integers is countable, because the number of possible algorithms is. The number of all functions from integers to integers is higher: the same as the cardinality of the real numbers.
	en.wikipedia.org /wiki/Function_(mathematics) (2999 words)

	Review of intervals and functions (Site not responding. Last check: 2007-10-07)
		For example, the domain of a function may be a set of complex numbers and the function may associate a set with each member of its domain.
		All the functions in this tutorial, however, have the two features, and the word "function" throughout means a rule that associates a number with every point in some subset of the set of n-vectors of numbers (where n may be 1).
		B is used for a function given by the rule f and the domain A whose range is a subset of B.
	www.chass.utoronto.ca /~osborne/MathTutorial/IAF.HTM (1468 words)

	Direct Manipulation Widgets (Site not responding. Last check: 2007-10-07)
		The three reasons for difficulty in transfer function specification, which were outlined in the previous section, can be considered in the context of a conceptual gap between the spatial and transfer function domains.
		The main role of the transfer function widget is to present a graphical representation of the transfer function domain, in which feedback from querying the volume (with the data probe or clipping plane) is displayed, and in which the transfer function itself can be set and altered.
		The balls at the corners of the transfer function widget are used to resize it, as with a desktop window, and the bars on the edges are used to translate its position.
	www.cs.utah.edu /~jmk/papers/vis01/node5.html (2693 words)

	[No title]
		In this way, a function may be thought of as a "machine" or a "fl box", converting a valid input into a unique output.
		numbers, the functional relationship is expressed by a formula, and the value of the function is obtained by direct substitution of the argument into the formula.
		element of the domain is associated to precisely one element of the codomain.
	en-cyclopedia.com /wiki/Function_(mathematics) (2581 words)

	Function Definitions
		A function is something that associates each element of a set with an element of another set (which may or may not be the same as the first set).
		Then the domain and codomain of this f are N, the image of, say 3, under this function is 9, and its range is the set of squares, i.e.
		Definition (composite function): Let g be a function from a set A to a set B, and let f be a function from B to a set C.
	www.cs.odu.edu /~toida/nerzic/content/function/definitions.html (841 words)

	Web-Hermes Chapter 4: Ingres domain function / mediator example.
		The function output type, in this case a relational database table, is computed by the built-in data function, which takes the file and field name inputs and assigns the output from the matching mediator data declaration.
		While relational databases are probably the most common domain class, the general domain function framework applies to many other types of software as well.
		After domain X exists within Hermes, then additional X domain data files can be integrated simply by writing the appropriate mediator data declarations which describe the underlying data structures (and is used ultimately to define the domain data function output type) of the new X files.
	www.cs.umd.edu /projects/hermes/UserManual/4-IngresExample.html (1429 words)

	1.2. Relations and Functions (Site not responding. Last check: 2007-10-07)
		Functions can be classified into three groups: those for which every element in the image has one preimage, those for which the range is the same as the image, and those which have both of these properties.
		A function f from A to B is called onto if for all b in B there is an a in A such that f(a) = b.
		A function f from A to B is called a bijection if it is one to one and onto, i.e.
	web01.shu.edu /projects/reals/logic/relation.html (615 words)

	Inverse Functions Lesson - II
		That is, the domain of the inverse is also "all real numbers", and the range of the inverse is also "all real numbers".
		With the domain restricted like this, the function does have an inverse that is also a function.
		Just about any time they give you a problem where they've taken the trouble to restrict the domain, you should take care with the algebra and draw a nice picture, because the inverse probably is a function, but it will probably take some extra effort to show this.
	www.purplemath.com /modules/invrsfcn2.htm (701 words)

	Math Forum - Ask Dr. Math Archives: Domain and Range of a Function (Site not responding. Last check: 2007-10-07)
		Determine the domain and range of the graph of "f" that starts at (- 2,3), goes down to (0,0), and ends at (3,4).
		Describe the range of the function g(x) = e^(-2x).
		Why is the domain of a function equal to the range of the inverse function?
	mathforum.org /library/drmath/sets/select/dm_domain_range.html (271 words)

	Calculus: The Function
		A function is defined as a set of ordered pairs (x,y) such that for every vaule of x, there is only one corresponding value for y.
		The range of a function is all the possible values for the function.
		The notation f(x) is used in polace of y to indicate the value of the function for a specific x.
	www.geocities.com /CapeCanaveral/7997/calculus1.html (247 words)

	Math Glossary A-M
		A critical number of a function f is a number c in the domain of f such that either f'(c)=0 or f'(c) does not exist.
		A function which cannot be drawn with a writing device without a gap or picking up of the writing device.
		Iteration is the repeated application of a function or process in which the output of each step is used as the input for the next iteration.
	www.blc.edu /fac/rbuelow/MPS/glossarya-m.htm (1780 words)

	All Elementary Mathematics - Study Guide - Functions and graphs - Basic notions and properties of functions...
		Now we can formulate a definition of a function more exactly: such a rule (law) of a correspondence between a set X and a set Y, that for each element of a set X one and only one element of a set Y can be found, is called a function.
		A graph of an even function is symmetrical relatively y-axis (Fig.5), a graph of an odd function is symmetrical relatively the origin of coordinates (Fig.6).
		Geometrically, a zero of a function is x-coordinate of a point of intersection of the function graph and x-axis.
	www.bymath.com /studyguide/fun/sec/fun6.htm (742 words)

	S _XFER S-Domain Transfer Function
		The s-domain transfer function includes gain and input offset parameters to allow for tailoring of the required signal.
		There are no limits on the internal signal values or on the output value of the s-domain transfer function, so you are cautioned to specify gain and coefficient values that will not cause the model to produce excessively large values.
		In AC analysis, the value returned is equal to the real and imaginary components of the total s-domain transfer function at each frequency of interest.
	www.cadmigos.com /manual/refman/rm0155.htm (441 words)

	Definition 1.2.2: Function, Domain, and Range (Site not responding. Last check: 2007-10-07)
		A function f from A to B is a relation between A and B such that for each a
		The set A is called the domain of the function, B is called its range.
		Often a function is denoted by y = f(x) or simply f(x), indicating the relation { (x,f(x)) }.
	www.shu.edu /projects/reals/logic/defs/function.html (61 words)

	Articles - Continuous function (Site not responding. Last check: 2007-10-07)
		Such a function can be represented by a graph in the Cartesian plane; the function is continuous if, roughly speaking, the graph is a single unbroken curve with no "holes" or "jumps": if it can be drawn by hand without lifting the pencil from the paper.
		Again consider a function f that maps a set of real numbers to another set of real numbers, and suppose c is an element of the domain of f.
		If a function has a domain which is not an interval, the notion of a continuous function as one whose graph you can draw without taking your pencil off the paper is not quite correct.
	gaple.com /articles/Continuous_function?mySession=0636f0d58fd255ba25... (1245 words)

	Mathematical Properties
		First, note that the Wigner function derived from a steady-state (4.56) or transient solution of (4.33) is purely real-valued, because both the Liouville equation (4.33) and the boundary conditions (4.36) are purely real.
		The Wigner function is obtained by transforming to the coordinates q and r, followed by a Fourier transform with respect to r.
		The domain of the Wigner function does not coincide with that of the system-system density operator, and the Wigner function domain extends into regions which describe system-reservoir correlations.
	www.utdallas.edu /~frensley/technical/opensyst/node20.html (2633 words)

	SparkNotes: SAT Math Level 1: Domain and Range
		The domain of a function is the set of inputs to the function that produce valid outputs.
		Some functions have different definitions for different intervals of their domains; this type of function is called a piecewise function.
		Occasionally the Math IC will present you with a question in which the domain of a function is restricted to a given interval, and you are asked to find the range of the newly restricted function.
	www.sparknotes.com /testprep/books/sat2/math1c/chapter10section5.rhtml (1525 words)

	Digital Filters - Frequency Filters
		The result in the spatial domain is equivalent to that of a smoothing filter; as the blocked high frequencies correspond to sharp intensity changes, i.e.
		We obtain the filter function of a bandpass by multiplying the filter functions of a lowpass and of a highpass in the frequency domain, where the cut-off frequency of the lowpass is higher than that of the highpass.
		To perform the frequency filtering we transform both the image of the house and the mask into the Fourier domain where we multiply the two images with the effect that the frequencies occurring in the mask remain in the output while the others are set to zero.
	homepages.inf.ed.ac.uk /rbf/HIPR2/freqfilt.htm (2854 words)

	Function domain (Site not responding. Last check: 2007-10-07)
		In mathematics, given a function f: A → B, the set A is called the domain, or domain of definition of f.
		A well-defined function must map every element of the domain to an element of its codomain.
		It is thus not a function on the set R of real numbers; R can't be its domain.
	www.city-search.org /fu/function-domain.html (373 words)

	The Domain and Range of a Function
		For example, the implicit domain of g is the interval [4,4).
		However, it is always possible to restrict the domain of a function to be something less than the implicit domain.
		We call the set of all inputs of a function its domain, and we call the set of all outputs of a function its range.
	jwbales.home.mindspring.com /precal/part1/part1.4.html (411 words)

	DsGetDcName (6 Parameters) function [Active Directory]
		Requires that the returned domain controller be a global catalog server for the forest of domains with this domain as the root.
		Requires that the returned domain controller be writable; that is, host a writable copy of the directory service, for Windows 2000 and later DCs, or of SAM (for DCs in operating systems prior to Windows 2000).
		No domain controller is available for the specified domain or the domain does not exist.
	msdn.microsoft.com /library/en-us/ad/ad/dsgetdcname.asp?frame=true (1450 words)

	SparkNotes: New SAT: Domain and Range
		The domain of a function is the set of inputs (x values) for which the function is defined.
		A function is therefore undefined for all the values of x for which division by zero occurs.
		The domain, which is all the valid values of x in the function, is the x-axis, while the range, all the values of f(x), is the y-axis.
	www.sparknotes.com /testprep/books/newsat/chapter19section13.rhtml (1182 words)

	Domain and Range
		Students use a graphing calculator to graph a continuous function and determine the domain and range of the function.
		Functions range from those with finite domains and ranges to those with infinite domains and ranges.
		Reveal to the class that the necessary window settings for x give the domain for the function, and those for y give the range for the function.
	www.glc.k12.ga.us /BuilderV03/lptools/lpshared/lpdisplay.asp?Session_Stamp=&LPID=25015 (746 words)

	The Wavelet Digest :: View topic - Question: Freq. domain transfer function of Daubechies finite support basis
		Hi, maybe I'm asking a wrong question, but I'm interested to know what is the frequency domain transfer function of Daubechies finite support basis.
		To make sense of my question, suppose, we have a finite support reactangle window in time domain, it will have a corresponding sinc-like frequency domain response which is, in freq.
		Note: in this case, we have the analytical expression of the transfer function.
	www.wavelet.org /phpBB2/viewtopic.php?t=5400&view=previous (152 words)

	[No title]
		Theorem: A function that is increasing throughout its domain is one-to-one.
		A function that is decreasing throughout its domain is one-to-one.
		Definition: Let f be a one-to-one function with domain D and range R. A function g with domain R and range D is the inverse function of f, provided the following condition is true for every x in D and every y in R: y=f(x) if and only if x=g(y).
	www.math.iupui.edu /~vvf/lecturenotes/lecture3_8.doc (294 words)

	[No title]
		In code generation domains, an important feature of the HOF stars is that they add no run-time overhead at all, since they self-destruct before code generation begins, and therefore do not appear in any form in the generated code.
		In functional languages, there is no syntactic difference between a function argument that is a data value, one that is a stream (an infinite sequence of data values), and one that is a function.
		Although in principle such higher-order functions can be designed in Ptolemy, their behavior would not be independent of their domain, so the HOF domain would be the wrong place for them.
	ptolemy.eecs.berkeley.edu /ptolemyclassic/almagest/docs/micro/html/hof.doc1.html (645 words)

	sdk8_grd (Site not responding. Last check: 2007-10-07)
		A base message string is the base string that was created with the add_string function, in the current domain and sub-domain, and with the specified name.
		The domain in which the message string should be found.
		If the translation specified in p_language is found, this function returns a message record based on domain, sub_domain, string name, and language name.
	www.oracle.com /technology/products/iportal/files/pdk105ea/plsql/doc/sdk8_grd.htm (202 words)

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