Recordings of the 4 minute mile being broken with the year of and the timings: ?

Question

Year: 1954, 1954, 1957, 1958,

Timings:(minutes and seconds) 3:59.4, 3:58.0, 3:57.2, 3:54.5

a. Is the timing a function of the year? OR

b. Is the year a function of the timing?

Please explain in as much detail as needed.

Answer 1

Generally, time-data is plotted with time as the independent variable (x-axis) and the results as the dependent variable (y-axis).  But a function requires none or only one unique y-value for each x-value and you have two  data points for the year 1954, so the data as shown does not represent a function.  Perhaps if the months or days were known and were different for the two 1954 values, then you would have a function.

With only the data shown however, to have a function, you would have to plot time on the x-axis and the year on the y-axis.  Separate independent (x-axis) values can have identical y-values, but every x-axis value can have no more than one y-value in order to represent a function.