One thing you can do is to plot the function and visually inspect it:
f = @(x)0.5*(sin(x)+abs(sin(x)));
fplot(f,[-pi pi])
It doesn't look even or odd.
You could also evaluate the function at some values of x and -x and compare the results:
x = -pi:0.1:pi;
is_even = isequal(f(x),f(-x))
is_odd = isequal(f(x),-f(-x))
(A sanity check with functions known to be odd or even)
f = @(x)sin(x);
is_even = isequal(f(x),f(-x))
is_odd = isequal(f(x),-f(-x))
f = @(x)cos(x);
is_even = isequal(f(x),f(-x))
is_odd = isequal(f(x),-f(-x))
