What is the background for $\sum_{k=1}^n|f(x_k)-f(x_{k-1})|$? The question is from the following problem:

If $f$ is the function whose graph is indicated in the figure above, then the least upper bound (supremum) of
$$\big\{\sum_{k=1}^n|f(x_k)-f(x_{k-1})|:0=x_0<x_1<\cdots<x_{n-1}<x_n=12\big\}$$
appears to be  
$A. 2\quad B. 7\quad C. 12\quad D. 16\quad E. 21$
I don't know what the set above means. And I am curious about the background of the set in real analysis. 

Total variation sums up how much a function bobs up and down. Yours does this 16 units.  Therefore choose D.
