  We study observational constraints on the cosmographic functions up to the
fourth derivative of the scale factor with respect to cosmic time, i.e., the
so-called snap function, using the non-parametric method of Gaussian Processes.
As observational data we use the Hubble parameter data. Also we use mock data
sets to estimate the future forecast and study the performance of this type of
data to constrains cosmographic functions. The combination between a
non-parametric method and the Hubble parameter data is investigated as a
strategy to reconstruct cosmographic functions. In addition, our results are
quite general because they are not restricted to a specific type of functional
dependency of the Hubble parameter. We investigate some advantages of using
cosmographic functions instead of cosmographic series, since the former are
general definitions free of approximations. In general, our results do not
deviate significantly from $\Lambda CDM$. We determine a transition redshift
$z_{tr}=-0.670^{+0.210}_{-0.120}$ with $H_{0}=67.44$ and
$z_{tr}=-0.710^{+0.159}_{-0.111}$ with $H_{0}=74.03$. Our main results are
summarized in table 2.
