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

[fivemack.livejournal.com]

Yes, f(x)=0 is the only function that is symmetric with respect to the X-axis, the requirement being f(x) = -f(x) (rather than f(x) = f(-x), which is symmetry with respect to the Y-axis, or f(x) = -f(-x), which is probably symmetry with respect to the line y=-x but which I'd just call an odd function)