  We present measurements of the optical and X-ray continua of 108 AGN (Seyfert 1s and quasars) from the Rosat International X-ray/Optical Survey (RIXOS). The sample covers a wide range in redshift (0<z<3.3), in X-ray spectral slope (-1.5 <ax<2.6) and in optical-to-X-ray ratio (0.4$<aox<1.5). A correlation is found between ax and aox; similar correlations have recently been reported in other X-ray and optical samples. We also identify previously unreported relationships between the optical slope (aopt) and ax (particularly at high redshifts) and between aopt and aox. These trends show that the overall optical-to-X-ray conti nuum changes from convex to concave as ax hardens, demonstrating a strong beha vioural link between the optical/UV big blue bump (BBB) and the soft X-ray ex cess, which is consistent with them being part of the same spectral component. By constructing models of the optical-to-X-ray continuum, we demonstrate that the observed correlations are consistent with an intrinsic spectrum which is ab sorbed through different amounts of cold gas and dust. The intrinsic spectrum is the sum of an optical-to-soft X-ray `big bump' component and an ax=1 power law; the column density of the cold gas ranges from 0 to ~4E21 cm-2 and the dust-to-gas ratio is assumed to be Galactic. The `big bump' may be represented by a T~1E6 K thermal bremsstrahlung or an accretion disk with a surrounding hot corona. The scatter in the data can accommodate a wide range in big bump tempe rature (or black hole mass) and strength. A source for the absorbing gas may be the dusty, molecular torus which lies beyond the broad line-emitting regions, although with a much lower column density than observed in Seyfert 2 galaxies. Alternatively, it may be the bulge of a spiral host galaxy or an elliptical host galaxy. 
Optical and X-ray properties of the RIXOS AGN: I - The continua