Question

Consider the constant function f(x) = 0. Determine whether the graph of this function is symmetric with respect to the x-axis, the y-axis, and/or the origin.

Answer 1

Well, it is the x-axis, so I don't think that would count as symmetry. If you divided the coordinate plane with y=x, then your function and the y-axis would have a symmetry across that line. Also, if you divide your function at the origin, it is symmetrical.

Answer 2

It's symmetric with respect to all those three. Let's see:
symmetric about y-axis: f(x) = 0 = f(-x)
symmetric about x-axis:\[f(x) = \pm(something)\ = \pm(0) = 0\]
symmetry about origin: f(x) = 0 = - f(-x)

Answer 3

Thank you Landon and K_Sameer73 for answering my question! Very helpful.