What does the range of a function represent?

The range of a function represents the set of all possible output values that the function can produce from its given input values. In other words, it includes the results you can obtain when you plug the input values into the function. For example, if you have a function that describes a relationship between x and y, the y-values that you can get after substituting various x-values into the function constitute the range.

Understanding the range is vital in various contexts, such as determining the behavior of functions in real-world scenarios, analyzing graphs, and solving equations. It helps in visualizing how changes in input affect the output and identifying the possible values that outputs can take, thereby playing a key role in the study of functions in mathematics.