Verify that the following is a coordinate function. EXAMPLE 3.2.15 Coordinate functions in the taxicab metric If is a nonvertical line in the Cartesian plane with equation y = mx + b, define f: R by f(x, y) = x(1+ |m|). If is a vertical line with equation x = a, define f by f(a, y) =y. The verification that these functions are coordinate functions in the taxicab metric is left as an exercise (Exercise 10). DEFINITION of a coordinate function Definition 3.2.13. Let be a line. A one-to-one correspondence f→R such that PQ f(P) f(Q) for every P and Q on & is called a coordinate function for the line l and the number f(P) is called the coordinate of the point P.