Question 136391
A function is even if {{{f(x)=f(-x)}}} for all x in the domain of f.  A function is odd if {{{-f(x)=f(-x)}}} for all x in the domain of f.  If neither equation holds across the domain, the function is neither even nor odd.


{{{f(-x)=-x-abs(-x)=-x-abs(x)<>x-abs(x)}}}.  Not even.


{{{-f(x)=-(x-abs(x))=-x+abs(x)<>-x-abs(x)=f(-x)}}}.  Not odd.



{{{
drawing(
600,600,-5,5,-5,5,
grid(1),
graph(
600,600,-5,5,-5,5,
x-abs(x),x-abs(x)
)
)
}}}


Note that the graph of the function is not symmetrical about the y-axis which it would be if it were even, nor is it symmetrical about the origin which it would be if it were odd.