heavy(x) = (1+sgn(x))/2
eps = .1
power = 2.
margin = .1
g(x) = heavy(x)*( heavy(x-eps)*(x-eps/2) + (1-heavy(x-eps))*x**2/(2*eps) )**power
f(x) = heavy(x)*( (x)**power )
h(x) = abs(x)**power
plot [-1:.5][-.1:5] f(x/margin+1), h(x/margin), 1


