  Being based on the only assumption that the universe is homogenous and
isotropic on large scales, cosmography is an ideal tool to investigate the
cosmic expansion history in a almost model-independent way. Fitting the data on
the luminosity distance and Baryon Acoustic Oscillations allows to determine
the confidence ranges for the cosmographic parameters hence giving some
quantitative constraints that a whatever theory has to fulfill. As an
application, we consider here the case of teleparallel gravity (TEGR) also
referred to as f(T)-gravity. To this end, we first work out analytical
expressions to express the present day values of f(T)-derivatives as a function
of the cosmographic parameters which hold under quite general and physically
motivated conditions. We then use the constraints coming from cosmography to
find out the confidence ranges for f(T)-derivatives up to the fifth order and
show how these can be used to check the viability of given TEGR models without
the need to explicitly solve the second order dynamic equations.
