Let $f:[a,b]\rightarrow\mathbb R$ be a real valued function If $f$ is not differentiable at a point say at $c$ then in the graph of $f$ we get a corner. So by looking at the graph we can say that whether $f$ is differentiable at a point or not. My question is can we detect whether a function $f$ is of bounded variation or not just by looking at it's graph? How can we relate bounded variation with graph.
We can also define functions of bounded variation for a function of real variables having complex valued image,i.e. for $f:[a,b]\rightarrow\mathbb C$ How can we do the same for above type of functions?