Range Of A Function (Noun)
Meaning
(mathematics) the set of values of the dependent variable for which a function is defined; "the image of f(x) = x^2 is the set of all non-negative real numbers if the domain of the function is the set of all real numbers".
Classification
Nouns denoting groupings of people or objects.
Examples
- The range of a function is the set of all possible output values it can produce for the given input values.
- In mathematics, the range of a function is often denoted as the image of the function, and it is a fundamental concept in understanding the behavior of functions.
- For the function f(x) = 1/x, the range of the function is the set of all non-zero real numbers, since the function is undefined at x = 0.
- The range of a function can be affected by the domain of the function, as illustrated by the example of the function f(x) = x^2, which has a range of all non-negative real numbers when the domain is the set of all real numbers.
- In some cases, the range of a function can be determined by analyzing the function's graph, as the range corresponds to the set of all y-values that the graph achieves.