Math question--hello, fivemack

[redbird]

This is, I think, more technicality/terminology than anything. One of my fellow editors ran into this:

Is y-0 [equivalently, f(x)=0] a function that is symmetric with respect to the x-axis?

It seems to me and her that it is, but a site she often finds reliable claims that there are no such functions.

[Note: this is a technical point, not that she and I have forgotten how to graph simple curves: y=x² is a function, but x=y² is not a function but a relation.]

ETA: Thank you all. Within a couple of hours, I was able to go back to Marta and tell her that I'd had responses from people I trusted, including a Ph.D. mathematician, and she and I were right and the web site was wrong. When she first asked me, after lunch, she wasn't going to consult her usual source because the manuscript is due Monday.

Comments

Definitions....?

[dragon3.livejournal.com]

If I recall correctly a function of x *must* have a *single* value for all values of x (except at singular points where the limit depends on the direction of approach -- think tan(pi/2))

If symmetry requires that every point have a corresponding point eqi-distant from the x axis in the opposite direction, then y=0 is not symmetric, as there is only a single point corresponding to each x value.

I'm not sure that there is a valuable answer. Certainly not without a rigorous definition of both function and symmetry. If anybody is really keen -- seek out Joukowski Transforms that will translate a circle into a flat line of finite length where there really are two y values for each x value, but both of them are zero, except where there is no y value ;-)