Is Y equals 0 an even or odd function?

f(x) = 0 is a constant function. This particular constant function is both even and odd.

Requirements for an even function: f(x) = f(-x) Geometrically, the graph of an even function is symmetric with respect to the y-axis The graph of a constant function is a horizontal line and will be symmetric with respect to the y-axis. y=0 or f(x)=0 is a constant function which is symmetric with respect to the y-axis. Requirements for an odd function:

-f(x) = f(-x) Geometrically, it is symmetric about the origin. While the constant function f(x)=0 is symmetric about the origin, constant function such as y=1 is not. and if we look at -f(x)=f(-x) for 1, we have -f(x)=-1 but f(-1)=1 since it is a constant function so y=1 is a constant function but not odd. So f(x)=c is odd if and only iff c=0 f(x)=0 is the only function which is both even and odd.