Codomain vs. Range: Know the Difference
By Shumaila Saeed || Updated on December 25, 2023
Codomain is the set of all possible outputs of a function, while Range is the actual set of outputs generated by the function.
Key Differences
Codomain refers to the entire set of potential outputs a function could possibly produce, regardless of whether every element is actually an output. Range, in contrast, is the subset of the codomain that consists of all elements that are actually outputs of the function.
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In mathematical functions, the Codomain is predefined and includes all values that could theoretically be returned, encompassing values that the function may never actually produce. The Range, however, is determined by the specific inputs used and includes only the values that the function actually returns.
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Codomain is a concept that helps define the scope of a function and is an essential part of a function's definition. Range is a result of the function's operation, representing the actual outcomes obtained when the function is applied to its domain.
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When visualizing functions, the Codomain can be thought of as the entire target space, while the Range represents the specific area within that space that the function actually maps to.
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Understanding the difference between Codomain and Range is crucial in advanced mathematics, especially in fields like calculus and linear algebra, where the distinction impacts the understanding of function behavior and properties.
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Comparison Chart
Definition
Set of potential outputs of a function
Actual outputs produced by the function
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Scope
Broader, includes all possible outputs
Narrower, limited to actual outputs
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Role in Functions
Part of a function's definition
Result of applying the function
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Visualization
Entire target space of a function
Specific area within the target space mapped by the function
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Codomain and Range Definitions
Codomain
Codomain is the complete set of potential outcomes of a function.
In the function y = x^2, the codomain includes all real numbers, as any real number could be the square of another.
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Range
Range is the actual set of values that a function produces.
The range of y = x^2 for x ≥ 0 is all non-negative real numbers.
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Codomain
Codomain is the set against which a function's outputs are compared.
In a probability function, the codomain is the range of probabilities from 0 to 1.
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Range
A number or grouping of things in the same category or within specified limits
Offers a range of financial services.
Jobs at different pay ranges.
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Codomain
Codomain is a theoretical construct that defines the scope of a function's output.
For a function mapping students to their grades, the codomain is all possible grades.
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Range
An amount or extent of variation
A wide price range.
The range of genetic diversity.
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Codomain
Codomain represents all conceivable results of a function, used in its formal definition.
The codomain of a function converting Celsius to Fahrenheit is all possible Fahrenheit temperatures.
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Range
(Music) The gamut of tones that a voice or instrument is capable of producing. Also called compass.
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Codomain
Codomain encompasses all values that a function could theoretically return.
The codomain of the sine function includes all values between -1 and 1.
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Codomain
A set containing all the values of a function. The range is a subset of the codomain.
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Range
Extent of perception, knowledge, experience, or ability
Calculus is simply out of my range.
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Codomain
The target set into which a function is formally defined to map elements of its domain; the set denoted Y in the notation f : X → Y.
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Range
The area or sphere in which an activity takes place
Beyond the range of the court's jurisdiction.
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Range
The maximum extent or distance limiting operation, action, or effectiveness, as of a sound, radio signal, instrument, firearm, or aircraft
The limited range of the telescope.
Out of range of their guns.
Within hearing range.
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Range
The maximum distance that can be covered by a vehicle with a specified payload before its fuel supply is exhausted.
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Range
A testing area at which rockets and missiles are launched and tracked.
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Range
The geographic region in which a plant, animal, or other organism normally lives or grows.
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Range
The opportunity or freedom to wander or explore
We had free range of the campus.
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Range
(Statistics) The difference or interval between the smallest and largest values in a frequency distribution or a set of data.
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Range
A group or series of things extending in a line or row, especially a row or chain of mountains.
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Range
A north-south strip of townships, each six miles square, numbered east and west from a specified meridian in a US public land survey.
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Range
To vary within specified limits
Sizes that range from small to extra large.
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Range
To cover or have application to a number of things
Their conversation ranged over the major issues of the day. Her responsibilities range across all aspects of the negotiations.
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Range
To move through, along, or around in an area or region
Raiders ranged up and down the coast.
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Range
To look over something or around an area or place
The teacher's eyes ranged over the class.
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Range
To live or grow within a particular region
"Some animals and plants range over a large portion of the world, yet retain the same character" (Charles Darwin).
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Range
To arrange or dispose in a particular order, especially in rows or lines
"In the front seats of the galleries were ranged the ladies of the court" (Carolly Erickson).
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Range
To assign to a particular category; classify
Her works are often ranged under the headings Mystery and Science Fiction.
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Range
To move through or along or around in (an area or region)
The scouts ranged the mountain forests. The patrol boat ranged the coast.
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Range
To look over or throughout (something)
His eyes ranged the room, looking for the letter.
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Range
(Nautical) To uncoil (an anchor cable) on deck so the anchor may descend easily.
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Range
A fireplace; a fire or other cooking apparatus; now specifically, a large cooking stove with many hotplates.
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Range
The distance from a person or sensor to an object, target, emanation, or event.
We could see the ship at a range of five miles.
One can use the speed of sound to estimate the range of a lightning flash.
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Range
The maximum distance or reach of capability (of a weapon, radio, detector, etc.).
This missile's range is 500 kilometres.
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Range
The distance a vehicle (e.g., a car, bicycle, lorry, or aircraft) can travel without refueling.
This aircraft's range is 15 000 kilometres.
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Range
The extent or space taken in by anything excursive; compass or extent of excursion; reach; scope.
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Range
(mathematics) The set of values (points) which a function can obtain.
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Range
(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.
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Range
The defensive area that a player can cover.
Jones has good range for a big man.
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Range
(music) The scale of all the tones a voice or an instrument can produce.
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Range
(ecology) The geographical area or zone where a species is normally naturally found.
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Range
(programming) A sequential list of values specified by an iterator.
Calls the given function on each value in the input range.
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Range
An aggregate of individuals in one rank or degree; an order; a class.
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Range
A wandering or roving; a going to and fro; an excursion; a ramble; an expedition.
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Range
In the public land system, a row or line of townships lying between two succession meridian lines six miles apart.
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Range
The variety of roles that an actor can play in a satisfactory way.
By playing in comedies as well as in dramas he has proved his range as an actor.
By playing in comedies as well as in dramas he has proved his acting range.
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Range
To exercise the power of something over something else; to cause to submit to, over.
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Range
(transitive) To bring (something) into a specified position or relationship (especially, of opposition) with something else.
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Range
(intransitive) Of a variable, to be able to take any of the values in a specified range.
The variable x ranges over all real values from 0 to 10.
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Range
(transitive) To classify.
To range plants and animals in genera and species
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Range
(intransitive) To form a line or a row.
The front of a house ranges with the street.
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Range
(intransitive) To be placed in order; to be ranked; to admit of arrangement or classification; to rank.
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Range
(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.
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Range
(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.
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Range
(biology) To be native to, or live in, a certain district or region.
The peba ranges from Texas to Paraguay.
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Range
To sail or pass in a direction parallel to or near.
To range the coast
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Range
(baseball) Of a player, to travel a significant distance for a defensive play.
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Range
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.
Maccabeus ranged his army by bands.
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Range
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.
It would be absurd in me to range myself on the side of the Duke of Bedford and the corresponding society.
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Range
To dispose in a classified or in systematic order; to arrange regularly; as, to range plants and animals in genera and species.
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Range
To rove over or through; as, to range the fields.
Teach him to range the ditch, and force the brake.
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Range
To sail or pass in a direction parallel to or near; as, to range the coast.
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Range
To rove at large; to wander without restraint or direction; to roam.
Like a ranging spaniel that barks at every bird he sees.
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Range
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.
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Range
To be placed in order; to be ranked; to admit of arrangement or classification; to rank.
And range with humble livers in content.
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Range
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.
Which way the forests range.
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Range
To be native to, or live in, a certain district or region; as, the peba ranges from Texas to Paraguay.
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Range
A series of things in a line; a row; a rank; as, a range of buildings; a range of mountains.
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Range
An aggregate of individuals in one rank or degree; an order; a class.
The next range of beings above him are the immaterial intelligences.
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Range
A kitchen grate.
He was bid at his first coming to take off the range, and let down the cinders.
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Range
An extended cooking apparatus of cast iron, set in brickwork, and affording conveniences for various ways of cooking; also, a kind of cooking stove.
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Range
A wandering or roving; a going to and fro; an excursion; a ramble; an expedition.
He may take a range all the world over.
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Range
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.
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Range
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.
Far as creation's ample range extends.
The range and compass of Hammond's knowledge filled the whole circle of the arts.
A man has not enough range of thought.
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Range
The horizontal distance to which a shot or other projectile is carried.
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Range
In the public land system of the United States, a row or line of townships lying between two successive meridian lines six miles apart.
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Range
An area in which something acts or operates or has power or control:
The range of a supersonic jet
The ambit of municipal legislation
Within the compass of this article
Within the scope of an investigation
Outside the reach of the law
In the political orbit of a world power
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Range
The limits within which something can be effective;
Range of motion
He was beyond the reach of their fire
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Range
A large tract of grassy open land on which livestock can graze;
They used to drive the cattle across the open range every spring
He dreamed of a home on the range
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Range
A series of hills or mountains;
The valley was between two ranges of hills
The plains lay just beyond the mountain range
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Range
A place for shooting (firing or driving) projectiles of various kinds;
The army maintains a missile range in the desert
Any good golf club will have a range where you can practice
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Range
The limits of the values a function can take;
The range of this function is the interval from 0 to 1
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Range
A variety of different things or activities;
He answered a range of questions
He was impressed by the range and diversity of the collection
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Range
A kitchen appliance used for cooking food;
Dinner was already on the stove
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Range
Change or be different within limits;
Estimates for the losses in the earthquake range as high as $2 billion
Interest rates run from 5 to 10 percent
The instruments ranged from tuba to cymbals
My students range from very bright to dull
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Range
Move about aimlessly or without any destination, often in search of food or employment;
The gypsies roamed the woods
Roving vagabonds
The wandering Jew
The cattle roam across the prairie
The laborers drift from one town to the next
They rolled from town to town
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Range
Have a range; be capable of projecting over a certain distance, as of a gun;
This gun ranges over two miles
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Range
Range or extend over; occupy a certain area;
The plants straddle the entire state
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Range
Assign a rank or rating to;
How would you rank these students?
The restaurant is rated highly in the food guide
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Range
Range consists of all outputs that a function actually generates.
In a function that squares integers, the range includes only perfect squares.
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Range
Range is the subset of the codomain that the function maps to.
For the sine function, the range is the set of values from -1 to 1.
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Range
Range is determined by applying the function to all elements in its domain.
The range of a function assigning students to classes is the actual classes assigned.
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Range
Range is the practical outcome of a function based on its input.
In a sales tax calculation function, the range is the set of possible tax amounts.
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Repeatedly Asked Queries
Is Codomain always larger than Range?
Often, but not necessarily; they can be equal.
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How does the concept of Codomain apply in calculus?
It helps define the limits and possibilities of function outputs.
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What is a Codomain?
A set of all possible outputs a function could produce.
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How is Range different from Codomain?
Range is the actual set of outputs a function produces, while Codomain includes all potential outputs.
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Can Codomain and Range be the same?
Yes, if a function's outputs cover all its potential outcomes.
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Does the Range depend on the function's input?
Yes, it is determined by the specific values the function is applied to.
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Do all functions have a Codomain?
Yes, every function is defined with a Codomain.
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Why is Codomain important in defining a function?
It sets the theoretical scope and possibilities of a function's output.
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How does changing the domain affect the Range?
Altering the domain can expand or limit the Range.
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Can functions have multiple Ranges?
No, each function has one Range based on its domain.
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How is Codomain used in linear algebra?
To define the scope of vector spaces and transformations.
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Can the Range of a function change?
Yes, it changes if the function's domain or formula changes.
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Why is understanding Range important?
It reveals the actual behavior and outputs of a function.
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Is Codomain a real-world concept or theoretical?
It's a theoretical concept with practical implications.
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Can Codomain be changed without altering the function?
No, changing the Codomain effectively changes the function.
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What is an example of a function with a limited Range?
The sine function, with a range between -1 and 1.
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Is the Codomain relevant in practical applications?
Yes, especially in predicting and understanding potential outcomes.
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Nov 23, 2023
What role does Range play in function analysis?
It helps in understanding the actual output and effectiveness of a function.
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Nov 23, 2023
Can Range be extended to match Codomain?
Only by altering the function or its domain.
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Does the Range always include all values in the Codomain?
No, it often includes only a subset of the Codomain.
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Nov 23, 2023
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About Author
Written by
Shumaila SaeedShumaila Saeed, an expert content creator with 6 years of experience, specializes in distilling complex topics into easily digestible comparisons, shining a light on the nuances that both inform and educate readers with clarity and accuracy.
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