Which of the following describes the range of a function?

The range of a function is defined as the collection of all possible outputs that the function can produce. This means if you consider every input (or x-coordinate) for the function, the range includes every resulting output (or y-coordinate). Understanding the concept of range is crucial because it tells us what values the dependent variable can take based on the given independent variable.

For example, if you have a function that takes any real number as input and outputs the square of that number, the range would be all non-negative real numbers because the square of any real number cannot be negative. This reflects the key characteristic of the range – it encompasses all potential values that result from applying the function to its entire domain.

This concept is foundational in mathematics as it allows for a comprehensive understanding of the behavior of functions and their graphs, facilitating further studies in calculus, algebra, and various applications in real-world scenarios.