The person walks 10 miles in total. If w represents the (variable) distance west she walks, and D represents her (variable) distance from home at the end of her walk, is D a function of w?
Yes. It is also a function of the other directions.
Something is “a function” of something else when the it requires the input/action/value/condition of that something else to determine its own current state. As in this example, a single “output” or result may be a “function” of MORE than one other variable.
In this example D is also a function of ‘e’, ‘n’ and ‘s’ representing the distance she walks East, North and South, respectively. The total miles walked is also a function of the four direction/distance variables, but it is NOT a function of D.