Domain vs. Range — What's the Difference?

Inputs within which a function is mathematically defined.

Set of all possible outputs from a function.

Set of all possible inputs for a function.

A subset of real numbers that results from the function’s operation.

The allowable x-values for any given function.

The complete set of values that y can take as outputs from a function.

A subset of real numbers that can be plugged into a function.

The actual outputs that a function can produce.

The complete set of values that x can take in a function.

Outputs derived from applying the domain to the function.

An area of territory owned or controlled by a particular ruler or government

The area of variation between upper and lower limits on a particular scale

A distinct subset of the Internet with addresses sharing a common suffix or under the control of a particular organization or individual.

A set of different things of the same general type

A discrete region of magnetism in ferromagnetic material.

The distance within which a person can see or hear

The set of possible values of the independent variable or variables of a function.

A line or series of mountains or hills

A distinct region of a complex molecule or structure.

A large area of open land for grazing or hunting

A territory over which rule or control is exercised.

A large cooking stove with burners or hotplates and one or more ovens, all of which are kept continually hot

A sphere of activity, influence, or knowledge

A row of buildings

The set of all possible values of an independent variable of a function.

The direction or position in which something lies

An open connected set that contains at least one point.

Vary or extend between specified limits

(Computers)A group of networked computers that share a common communications address.

Place or arrange in a row or rows or in a specified manner

(Physics)Any of numerous contiguous regions in a ferromagnetic material in which the direction of spontaneous magnetization is uniform and different from that in neighboring regions.

Place oneself or be placed in opposition to (a person or group)

(Biology)Any of three primary divisions of organisms, consisting of the eukaryotes, bacteria, and archaea, that rank above a kingdom in taxonomic systems based on similarities of DNA sequences.

(of a person or animal) travel or wander over a wide area

(Law)The land of one with paramount title and absolute ownership.

Obtain the range of a target by adjustment after firing past it or short of it, or by the use of radar or laser equipment

A geographic area owned or controlled by a single person or organization.

(of a person or their lifestyle) orderly; settled

A field or sphere of activity, influence or expertise.

A number or grouping of things in the same category or within specified limits

A group of related items, topics, or subjects.

An amount or extent of variation

(mathematics) The set of all possible mathematical entities (points) where a given function is defined.

(Music) The gamut of tones that a voice or instrument is capable of producing. Also called compass.

The set of input (argument) values for which a function is defined.

A class, rank, or order

(mathematics) A ring with no zero divisors; that is, in which no product of nonzero elements is zero.

Extent of perception, knowledge, experience, or ability

An open and connected set in some topology. For example, the interval (0,1) as a subset of the real numbers.

The area or sphere in which an activity takes place

Any DNS domain name, particularly one which has been delegated and has become representative of the delegated domain name and its subdomains.

The maximum extent or distance limiting operation, action, or effectiveness, as of a sound, radio signal, instrument, firearm, or aircraft

A collection of DNS or DNS-like domain names consisting of a delegated domain name and all its subdomains.

The maximum distance that can be covered by a vehicle with a specified payload before its fuel supply is exhausted.

(computing) A collection of information having to do with a domain, the computers named in the domain, and the network on which the computers named in the domain reside.

The distance between a projectile weapon and its target.

(computing) The collection of computers identified by a domain's domain names.

A place equipped for practice in shooting at targets.

(physics) A small region of a magnetic material with a consistent magnetization direction.

A testing area at which rockets and missiles are launched and tracked.

(computing) Such a region used as a data storage element in a bubble memory.

A place or business where golf shots can be practiced.

(data processing) A form of technical metadata that represent the type of a data item, its characteristics, name, and usage.

An extensive area of open land on which livestock wander and graze.

(taxonomy) The highest rank in the classification of organisms, above kingdom; in the three-domain system, one of the taxa Bacteria, Archaea, or Eukaryota.

The geographic region in which a plant, animal, or other organism normally lives or grows.

(biochemistry) A folded section of a protein molecule that has a discrete function; the equivalent section of a chromosome

The opportunity or freedom to wander or explore

Dominion; empire; authority.

(Mathematics) The set of all values a given function may take on.

The territory over which dominion or authority is exerted; the possessions of a sovereign or commonwealth, or the like. Also used figuratively.

(Statistics) The difference or interval between the smallest and largest values in a frequency distribution or a set of data.

Landed property; estate; especially, the land about the mansion house of a lord, and in his immediate occupancy; demesne.

A group or series of things extending in a line or row, especially a row or chain of mountains.

Ownership of land; an estate or patrimony which one has in his own right; absolute proprietorship; paramount or sovereign ownership.

One of a series of double-faced bookcases in a library stack room.

The set of values which the independent variable of a function may take. Contrasted to range, which is the set of values taken by the dependent variable.

A north-south strip of townships, each six miles square, numbered east and west from a specified meridian in a US public land survey.

A connected set of points, also called a region.

A stove with spaces for cooking a number of things at the same time.

A region within a ferromagnetic material, composed of a number of atoms whose magnetic poles are pointed in the same direction, and which may move together in a coordinated manner when disturbed, as by heating. The direction of polarity of adjacent domains may be different, but may be aligned by a strong external magnetic field.

To vary within specified limits

An address within the internet computer network, which may be a single computer, a network of computers, or one of a number of accounts on a multiuser computer. The domain specifies the location (host computer) to which communications on the internet are directed. Each domain has a corresponding 32-bit number usually represented by four numbers separated by periods, as 128.32.282.56. Each domain may also have an alphabetical name, usually composed of a name plus an extension separated by a period, as worldsoul.org; the alphabetical name is referred to as a domain name.

To extend in a particular direction

The three-dimensional structure within an immunoglobulin which is formed by one of the homology regions of a heavy or light chain.

To cover or have application to a number of things

The field of knowledge, expertise, or interest of a person; as, he had a limited domain of discourse; I can't comment on that, it's outside my domain.

To move through, along, or around in an area or region

A particular environment or walk of life.

To wander freely; roam

People in general; especially a distinctive group of people with some shared interest.

To look over something or around an area or place

A particular environment or walk of life;

To live or grow within a particular region

Territory over which rule or control is exercised;

To arrange or dispose in a particular order, especially in rows or lines

The set of values of the independent variable for which a function is defined

To assign to a particular category; classify

People in general; especially a distinctive group of people with some shared interest;

To move through or along or around in (an area or region)

A knowledge domain that you are interested in or are communicating about;

To look over or throughout (something)

To turn (livestock) onto an extensive area of open land for grazing.

To align (a gun, for example) with a target.

To determine the distance of (a target).

To be capable of reaching (a maximum distance).

(Nautical) To uncoil (an anchor cable) on deck so the anchor may descend easily.

A line or series of mountains, buildings, etc.

A fireplace; a fire or other cooking apparatus; now specifically, a large cooking stove with many hotplates.

Selection, array.

An area for practicing shooting at targets.

An area for military training or equipment testing.

The distance from a person or sensor to an object, target, emanation, or event.

The maximum distance or reach of capability (of a weapon, radio, detector, etc.).

The distance a vehicle (e.g., a car, bicycle, lorry, or aircraft) can travel without refueling.

An area of open, often unfenced, grazing land.

The extent or space taken in by anything excursive; compass or extent of excursion; reach; scope.

(mathematics) The set of values (points) which a function can obtain.

(statistics) The length of the smallest interval which contains all the data in a sample; the difference between the largest and smallest observations in the sample.

The defensive area that a player can cover.

(music) The scale of all the tones a voice or an instrument can produce.

(ecology) The geographical area or zone where a species is normally naturally found.

(programming) A sequential list of values specified by an iterator.

An aggregate of individuals in one rank or degree; an order; a class.

(obsolete) The step of a ladder; a rung.

A bolting sieve to sift meal.

A wandering or roving; a going to and fro; an excursion; a ramble; an expedition.

In the public land system, a row or line of townships lying between two succession meridian lines six miles apart.

The variety of roles that an actor can play in a satisfactory way.

(intransitive) To travel over (an area, etc); to roam, wander.

(transitive) To rove over or through.

To exercise the power of something over something else; to cause to submit to, over.

(transitive) To bring (something) into a specified position or relationship (especially, of opposition) with something else.

(intransitive) Of a variable, to be able to take any of the values in a specified range.

(transitive) To classify.

(intransitive) To form a line or a row.

(intransitive) To be placed in order; to be ranked; to admit of arrangement or classification; to rank.

(transitive) To set in a row, or in rows; to place in a regular line or lines, or in ranks; to dispose in the proper order.

(transitive) To place among others in a line, row, or order, as in the ranks of an army; usually, reflexively and figuratively, to espouse a cause, to join a party, etc.

(biology) To be native to, or live in, a certain district or region.

To determine the range to a target.

To sail or pass in a direction parallel to or near.

(baseball) Of a player, to travel a significant distance for a defensive play.

To set in a row, or in rows; to place in a regular line or lines, or in ranks; to dispose in the proper order; to rank; as, to range soldiers in line.

To place (as a single individual) among others in a line, row, or order, as in the ranks of an army; - usually, reflexively and figuratively, (in the sense) to espouse a cause, to join a party, etc.

To separate into parts; to sift.

To dispose in a classified or in systematic order; to arrange regularly; as, to range plants and animals in genera and species.

To rove over or through; as, to range the fields.

To sail or pass in a direction parallel to or near; as, to range the coast.

To be native to, or to live in; to frequent.

To rove at large; to wander without restraint or direction; to roam.

To have range; to change or differ within limits; to be capable of projecting, or to admit of being projected, especially as to horizontal distance; as, the temperature ranged through seventy degrees Fahrenheit; the gun ranges three miles; the shot ranged four miles.

To be placed in order; to be ranked; to admit of arrangement or classification; to rank.

To have a certain direction; to correspond in direction; to be or keep in a corresponding line; to trend or run; - often followed by with; as, the front of a house ranges with the street; to range along the coast.

To be native to, or live in, a certain district or region; as, the peba ranges from Texas to Paraguay.

A series of things in a line; a row; a rank; as, a range of buildings; a range of mountains.

An aggregate of individuals in one rank or degree; an order; a class.

The step of a ladder; a rung.

A kitchen grate.

An extended cooking apparatus of cast iron, set in brickwork, and affording conveniences for various ways of cooking; also, a kind of cooking stove.

A bolting sieve to sift meal.

A wandering or roving; a going to and fro; an excursion; a ramble; an expedition.

That which may be ranged over; place or room for excursion; especially, a region of country in which cattle or sheep may wander and pasture.

Extent or space taken in by anything excursive; compass or extent of excursion; reach; scope; discursive power; as, the range of one's voice, or authority.

The region within which a plant or animal naturally lives.

The horizontal distance to which a shot or other projectile is carried.

In the public land system of the United States, a row or line of townships lying between two successive meridian lines six miles apart.

See Range of cable, below.

An area in which something acts or operates or has power or control:

The limits within which something can be effective;

A large tract of grassy open land on which livestock can graze;

A series of hills or mountains;

A place for shooting (firing or driving) projectiles of various kinds;

The limits of the values a function can take;

A variety of different things or activities;

The limit of capability;

A kitchen appliance used for cooking food;

Change or be different within limits;

Move about aimlessly or without any destination, often in search of food or employment;

Have a range; be capable of projecting over a certain distance, as of a gun;

Range or extend over; occupy a certain area;

Lay out in a line

Feed as in a meadow or pasture;

Let eat;

Assign a rank or rating to;

Yes, some functions, like f(x) = x, have the same domain and range, which can be all real numbers.

A graph helps visually identify the domain as the set of all x-values taken by the graph and the range as all y-values the graph reaches.

Generally, yes, the range of a continuous function is also continuous if the domain is continuous.

The domain is the set of all possible input values, while the range is the set of all outputs produced by these inputs.

To find the domain of a complex function, identify values that do not lead to undefined operations like division by zero, negative square roots, or logarithms of non-positive numbers.

Yes, every function by definition has a domain and a range, though identifying them can sometimes be complex.

Restricting the domain limits the set of possible inputs, which can reduce or alter the range of possible outputs.

Graphing calculators, algebraic software, and plotting tools are useful in visualizing functions to determine their domain and range.

The type of function (polynomial, rational, trigonometric, etc.) dictates the nature of potential inputs (domain) and outputs (range).

Common mistakes include forgetting to exclude values that make the function undefined and misinterpreting the extent of outputs.

Understanding these helps in correctly applying the function in calculations, graphing, and solving real-world problems.

Asymptotes are lines that a graph approaches but never touches. Vertical asymptotes often restrict the domain (e.g., undefined points), and horizontal asymptotes can suggest limits in the range.

No, functions can have infinite domains and ranges, such as linear functions or exponential functions.

While the domain is chosen independently based on function properties, the range is directly dependent on the domain and the function's behavior.

In statistics, the domain might refer to the range of possible data values (input), and the range could be the possible outcomes of a statistical function or model.