What does the "range" of a function represent?

The range of a function specifically represents the set of outputs that can be generated by that function when all possible inputs are considered. It includes all the values that the dependent variable (usually denoted as ( y ) in a function ( f(x) )) can take as ( x ) varies over its domain. Understanding the range helps in analyzing how the function behaves and what values it can produce. In mathematical terms, if you have a function defined as ( f: X \rightarrow Y ), the range consists of all ( f(x) ) for ( x ) in the set ( X ) (the domain).

This concept is crucial in various applications, including optimization problems and understanding the limits of a function's behavior. By identifying the range, one can gain insights into the characteristics of the function, such as whether it is bounded or unbounded, continuous or discrete, etc.