I would like to understand, why must we sort the x axis or y axis in order when trying to plot a function $y=f(x)$. Why would using an un-ordered $x$-axis be the wrong depiction of relationship between $x$ and $y$?
I'm aware this must be pretty stupid of a question, but I cannot seem to find a reason. I understand that for categorical values (think histogram of cars owned vs number of people, bucket (0-3) etc will still help me understand how many people own how many cars, regardless of whether the bucket is ordered or not, could be 0-3 then 10-13 then 5-8) the order of say x-axis values doesn't matter, but why do we say that we won't be able to understand trend or characteristics of distribution of values if the axes were not ordered (ascending or descending)?
Also, does a normal distribution also requires correct $x$-axis ordering? I could just find probability for a range through pdf and plot it randomly, would that violate the area under curve of $1$?