Let's say I have a function $f(x)$ and an empirical approximation of the function $\tilde{f}(x)$. I cannot prove mathematically that errors is in certain bound. However, when I plot the error, the error is in certain bound. Do you accept that graph as a proof?
ps. my functions are $f(x) = \frac{\cos(x)}{x-x\sin(x)} $ and $\tilde{f}(x) = \frac{1}{x}+\frac{4}{\pi(\pi/2-x)}+0.18733-0.01x$. The goal is to show $|\frac{f(x)-\tilde{f}(x)}{f(x)}|<2\times 10^{-4}$ when $0<x<\pi/2$.
I certainly would not and I doubt any analyst worth his or her salt would on an exam, let alone a publishable paper. A graph can certainly motivate a proof,but the graph in and of itself certainly wouldn't be a proof. It certainly shouldn't be accepted as one and you're not doing the paper's author any favors by doing so. Send it back to him or her and tell him(her) back to the drawing board.