  We study an improved three-dimensional Ising model with external magnetic
field near the critical point by Monte Carlo simulations. From our data we
determine numerically the universal scaling functions of the magnetization,
that is the equation of state, of the susceptibility and of the correlation
length. In order to normalize the scaling functions we calculate the critical
amplitudes of the three observables on the critical line, the phase boundary
and the critical isochore. These amplitudes lead to the universal ratios
C^+/C^-=4.756(28), R_{chi}=1.723(13), Q_c=0.326(3) and Q_2=1.201(10). We find
excellent agreement of the data with the parametric representation of the
asymptotic equation of state as found by field theory methods. The comparison
of the susceptibility data to the corresponding scaling function shows a
marginal difference in the symmetric phase, which can be explained by the
slightly different value for R_{chi} used in the parametrization. The shape of
the correlation-length-scaling function is similar to the one of the
susceptibility, as expected from earlier parametrizations. The peak positions
of the two scaling functions are coinciding within the error bars.
