Understanding the Range in Mathematics: Definition, Examples, and Importance

Range

In mathematics, the range refers to the set of all possible values that a function or a set of data can take on

In mathematics, the range refers to the set of all possible values that a function or a set of data can take on. It represents the difference between the largest and smallest values within a particular set.

For a function, the range is the set of all output values that the function can produce. It is the collection of all possible y-values corresponding to the x-values in the domain of the function. To find the range, first determine the domain of the function (the set of input values), and then evaluate the function for each value in the domain to find the corresponding output values. The range is then the set of all these output values.

For example, consider the function f(x) = x^2, where the domain is all real numbers. To find the range of this function, we square each input value and obtain the corresponding output value. Since squaring a real number always results in a non-negative value, the range of this function is all non-negative real numbers, or [0, ∞).

For a set of data, the range represents the difference between the maximum and minimum values in the set. It provides information about the spread, variability, or dispersion of the data. To find the range of a set of data, simply subtract the smallest value from the largest value.

For example, consider the set of data: {2, 5, 10, 8, 6}. To find the range, we subtract the smallest value (2) from the largest value (10), giving us a range of 10 – 2 = 8.

It’s worth noting that the range can sometimes be limited by the domain of the function or by the nature of the given data set. In some cases, the range may be all real numbers, while in other cases, it may be restricted to a specific interval or a finite set of values.

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