dependent variable

The dependent variable is the one that responds. You do not set it directly; it is whatever the function gives back once you have chosen the input. In y = f(x), the letter y is the dependent variable — its value waits on your choice of x.

It is called dependent precisely because it depends on the independent variable. Change the input and the output may change with it; the dependent variable carries the function's answer. By convention it is usually plotted along the vertical axis.

This is the same idea as the range, viewed from a different angle. The set of all values the dependent variable can take, as the input ranges over the domain, is exactly the range of the function. So the dependent variable is the live quantity whose collected values form the range.