All Topics  
Range (mathematics)

 

 
   Email Print
   Bookmark   Link
 

 

Range (mathematics)
 
 
  Topics Range (mathematics) Topic Home

In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, the range of a function
Function (mathematics)

The mathematical concept of a function expresses dependence between two quantities, one of which is known and the other which is produced. A function associates a single output to each input element drawn from a fixed Set , such as the real numbers , although different inputs may have the same output....
 is the set of all "output" values produced by that function. Sometimes it is called the image
Image (mathematics)

In mathematics, the image of a set under a given function is the set of all possible function outputs when taking each element of the set, successively, as the function's argument....
, or more precisely, the image of the domain of the function. If a function is a surjection then its range is equal to its codomain
Codomain

In mathematics, the codomain, range or target set, of a function , described symbolically as ' : ' ? ', is the set ' into which all of the output of the function is constrained to fall....
. In a representation of a function in an xy Cartesian coordinate system
Cartesian coordinate system

In mathematics, the Cartesian coordinate system is used to determine each Point uniquely in a Plane through two numbers, usually called the x-coordinate or abscissa and the y-coordinate or ordinate of the point....
, the range is represented on the ordinate (on the y axis).

Sometimes the range means the set of all possible values, i.e.






Discussion
Ask a question about 'Range (mathematics)'
Start a new discussion about 'Range (mathematics)'
Answer questions from other users
Full Discussion Forum



Encyclopedia


In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, the range of a function
Function (mathematics)

The mathematical concept of a function expresses dependence between two quantities, one of which is known and the other which is produced. A function associates a single output to each input element drawn from a fixed Set , such as the real numbers , although different inputs may have the same output....
 is the set of all "output" values produced by that function. Sometimes it is called the image
Image (mathematics)

In mathematics, the image of a set under a given function is the set of all possible function outputs when taking each element of the set, successively, as the function's argument....
, or more precisely, the image of the domain of the function. If a function is a surjection then its range is equal to its codomain
Codomain

In mathematics, the codomain, range or target set, of a function , described symbolically as ' : ' ? ', is the set ' into which all of the output of the function is constrained to fall....
. In a representation of a function in an xy Cartesian coordinate system
Cartesian coordinate system

In mathematics, the Cartesian coordinate system is used to determine each Point uniquely in a Plane through two numbers, usually called the x-coordinate or abscissa and the y-coordinate or ordinate of the point....
, the range is represented on the ordinate (on the y axis).

Sometimes the range means the set of all possible values, i.e. the codomain. This is also the current usage for range in computer science
Range (computer science)

In computer science, the term range may refer to one of two things:# The maximum and minimum values that may be stored in a variable.# The upper and lower bounds of an array....
.

Many ranges are of the form of an interval
Interval (mathematics)

In mathematics, a interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set....
, e.g. [0,1) for the numbers from 0 to 1 including 0 and excluding 1. Thus intervals are often referred to as ranges. The difference between the highest and lowest members of a set of numbers may also be referred to as a range, see range in statistics
Range (statistics)

In descriptive statistics, the range is the length of the smallest interval which contains all the data. It is calculated by subtracting the smallest observation from the greatest and provides an indication of statistical dispersion....
.

Examples


Let f be a function on the real numbers defined by . This function takes as input any real number and multiplies it by two. Multiplication by any real number can yield any real number, therefore f(x) may be any real number, which is to say that the range of f is (-8, 8).

In other instances, range may be restricted by the domain of the function. Consider the function g such that . Since the codomain
Codomain

In mathematics, the codomain, range or target set, of a function , described symbolically as ' : ' ? ', is the set ' into which all of the output of the function is constrained to fall....
 is , any real number is a legal value for g(x). However, the domain of g is , so the input for g may only be a real number greater than zero. Multiplying any positive real number by two will always yield another positive real number, so the range of g is (0, 8). Note here that the range of the function is not equal to its codomain, though the range is (and always will be) a subset of the codomain.

Range may also be restricted by the definition of the function. Consider the function h such that . Here the input is again any real number, though squaring
Exponentiation

Exponentiation is a mathematics operation , written 'an', involving two numbers, the base a and the exponent n....
 any real number will never yield a negative number, and so the output of h may be any nonnegative number (including zero), thus the range is [0, 8).

See also

  • Domain (mathematics)
    Domain (mathematics)

    In mathematics, the domain of a given function is the set of "input" values for which the function is defined. For instance, the domain of cosine would be all real numbers, while the domain of the square root would be only numbers greater than or equal to 0 ....
  • Bijection, injection and surjection
    Bijection, injection and surjection

    In mathematics, injections, surjections and bijections are classes of function distinguished by the manner in which parameter and are related or mapped to each other....
  • Rescaled range
    Rescaled range

    The rescaled range is a statistical measure of the variability of a time series introduced by the British hydrologist Harold Edwin Hurst . Its purpose is to provide an assessment of how the apparent variability of a series changes with the length of the time-period being considered....
  • Sequence
    Sequence

    In mathematics, a sequence is an ordered list of objects . Like a Set , it contains Element , and the number of terms is called the length of the sequence....
  • Range of a matrix