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In mathematics, the range of a function is the set of all "output" values produced by that function. Sometimes it is called the image, or more precisely, the image of the domain of the function. Range is also occasionally used to indicate the difference between the largest and smallest numbers in a set of real-valued data. Image File history File links Merge-arrows. ...
In mathematics, the image of an element x in a set X under the function f : X → Y, denoted by f(x), is the unique y in Y that is associated with x. ...
For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ...
Graph of example function, The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary (the independent variable, argument of the function, or its input) and the other as secondary (the value of the function, or output). A...
Output is the term denoting either an exit or changes which exits a system and which activate/modify a process. ...
In mathematics, the image of an element x in a set X under the function f : X → Y, denoted by f(x), is the unique y in Y that is associated with x. ...
In mathematics, the domain of a function is the set of all input values to the function. ...
In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ...
Examples
Let the function f be a function on the real numbers: In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ...
 defined by - f(x) = x2.
The codomain of f is R, and f takes all nonnegative values but never takes negative values, and thus the range is in fact the set R+—non-negative reals, i.e. the interval [0,∞): A codomain in mathematics is the set of output values associated with (or mapped to) the domain of inputs in a function. ...
A negative number is a number that is less than zero, such as −3. ...
A negative number is a number that is less than zero, such as −3. ...
In mathematics, interval is a concept relating to the sequence and set-membership of one or more numbers. ...
 Now let g be a function on the real numbers: In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ...
 defined by - g(x) = 2x.
In this case the image of g equals R, its codomain, since, for any real number y, - g(y / 2) = y.
In other words, g is onto R.
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