What does range mean in math?

In mathematics, the "range" refers to the set of all possible values that a function or a relation can take as output. It is determined by looking at the values that the function can produce when the input (also called the domain) varies over its possible values.

For example, if you have a function f(x), the range is the set of all possible values of f(x) for every input x in the domain.

To further illustrate, let's consider a simple example:

If f(x) = x², and the domain is all real numbers, the range would be all non-negative real numbers, because squaring any real number (whether positive or negative) results in a non-negative value.

For a set of numbers or data, the range is also defined as the difference between the largest and smallest values. For example, if you have the set of numbers {3, 5, 8, 12}, the range is 12 - 3 = 9.

In summary:

The range of a function is the set of all possible output values.
The range of a data set is the difference between the maximum and minimum values.