max(f, g) is computing max(f, -g)

[cbm755]

x  = chebfun(@(x) x, [-pi, 2*pi]);  f = exp(sin(2*x))

h = max(f, 1)

looks correct like this:

But:

h = max(f, 1 + 0.05*x)

looks like this:

I suspect something about conjugte transposes...